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I am playing around with OpenGL and one thing I decided to do is create my own Matrix class, instead of using glm's matrices.
The Matrix class has methods for translating, rotating and scaling the object, which are written below:
Matrix4 Matrix4::translate(Matrix4& matrix, Vector3& translation)
{
Vector4 result(translation, 1.0f);
result.multiply(matrix);
matrix.mElements[3 * 4 + 0] = result.x;
matrix.mElements[3 * 4 + 1] = result.y;
matrix.mElements[3 * 4 + 2] = result.z;
return matrix;
}
Matrix4 Matrix4::rotate(Matrix4& matrix, float angle, Vector3& axis)
{
if (axis.x == 0 && axis.y == 0 && axis.z == 0)
return matrix;
float r = angle;
float s = sin(r);
float c = cos(r);
float omc = 1.0f - cos(r);
float x = axis.x;
float y = axis.y;
float z = axis.z;
matrix.mElements[0 + 0 * 4] = c + x * x * omc;
matrix.mElements[1 + 0 * 4] = x * y * omc - z * s;
matrix.mElements[2 + 0 * 4] = z * x * omc + y * s;
matrix.mElements[0 + 1 * 4] = x * y * omc + z * s;
matrix.mElements[1 + 1 * 4] = c + y * y * omc;
matrix.mElements[2 + 1 * 4] = z * y * omc - x * s;
matrix.mElements[0 + 2 * 4] = x * z * omc - y * s;
matrix.mElements[1 + 2 * 4] = y * z * omc + x * s;
matrix.mElements[2 + 2 * 4] = c + z * z * omc;
return matrix;
}
Matrix4 Matrix4::scale(Matrix4& matrix, Vector3& scaler)
{
matrix.mElements[0 + 0 * 4] *= scaler.x;
matrix.mElements[1 + 0 * 4] *= scaler.x;
matrix.mElements[2 + 0 * 4] *= scaler.x;
matrix.mElements[0 + 1 * 4] *= scaler.y;
matrix.mElements[1 + 1 * 4] *= scaler.y;
matrix.mElements[2 + 1 * 4] *= scaler.y;
matrix.mElements[0 + 2 * 4] *= scaler.z;
matrix.mElements[1 + 2 * 4] *= scaler.z;
matrix.mElements[2 + 2 * 4] *= scaler.z;
matrix.mElements[3 + 3 * 4] = 1;
return matrix;
}
When I call the translate, rotate and scale methods in while loop (in this particular order), it does what I want, which is translate the object, then rotate it around its local origin and scale it. However, when I want to switch order so I call rotation first and then translation, I want it to do this:
But my code dosen't do that. Instead, its doing this:
What can I do so that my object only rotates around the center of the screen and not around it's local origin aswell?
My only guess is that I am doing something wrong with adding the rotation calculation on transformed matrix, but I still can't tell what it is.
EDIT: One thing i need to point out is if i left out the rotation method and i only tackle with translation and scaling, they do what i expect them to do in translation first, rotation second and in rotation first, translation second order.
EDIT 2: Here is how i call these functions in while loop.
Matrix4 trans = Matrix4(1.0f);
trans = Matrix4::rotate(trans, (float)glfwGetTime(), Vector3(0.0f, 0.0f, 1.0f));
trans = Matrix4::translate(trans, Vector3(0.5f, -0.5f, 0.0f));
trans = Matrix4::scale(trans, Vector3(0.5f, 0.5f, 1.0f));
shader.setUniformMatrix4f("uTransform", trans);
You have to concatenate the matrices by a matrix multiplication.
A matrix multiplication C = A * B works like this:
Matrix4x4 A, B, C;
// C = A * B
for ( int k = 0; k < 4; ++ k )
for ( int j = 0; j < 4; ++ j )
C[k][j] = A[0][j] * B[k][0] + A[1][j] * B[k][1] + A[2][j] * B[k][2] + A[3][j] * B[k][3];
I recommend to create specify the matrix class somehow like this:
#include <array>
class Matrix4
{
public:
std::array<float, 16> mElements{
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1 };
const float * dataPtr( void ) const { return mElements.data(); }
Matrix4 & multiply( const Matrix4 &mat );
Matrix4 & translate( const Vector3 &translation );
Matrix4 & scale( const Vector3 &scaler );
Matrix4 & rotate( float angle, const Vector3 &axis );
};
Implement the matrix multiplication. Note, you have to store the result in a buffer.
If you would write the result back to the matrix member directly, then you would change elements, which will read again later in the nested loop and the result wouldn't be correct:
Matrix4& Matrix4::multiply( const Matrix4 &mat )
{
// multiply the existing matrix by the new and store the result in a buffer
const float *A = dataPtr();
const float *B = mat.dataPtr();
std::array<float, 16> C;
for ( int k = 0; k < 4; ++ k ) {
for ( int j = 0; j < 4; ++ j ) {
C[k*4+j] =
A[0*4+j] * B[k*4+0] +
A[1*4+j] * B[k*4+1] +
A[2*4+j] * B[k*4+2] +
A[3*4+j] * B[k*4+3];
}
}
// copy the buffer to the attribute
mElements = C;
return *this;
}
Adapt the methods for translation, rotation and scaling like this:
Matrix4 & Matrix4::translate( const Vector3 &translation )
{
float x = translation.x;
float y = translation.y;
float z = translation.z;
Matrix4 transMat;
transMat.mElements = {
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
x, y, z, 1.0f };
return multiply(transMat);
}
Matrix4 & Matrix4::rotate( float angle, const Vector3 &axis )
{
float x = axis.x;
float y = axis.y;
float z = axis.z;
float c = cos(angle);
float s = sin(angle);
Matrix4 rotationMat;
rotationMat.mElements = {
x*x*(1.0f-c)+c, x*y*(1.0f-c)-z*s, x*z*(1.0f-c)+y*s, 0.0f,
y*x*(1.0f-c)+z*s, y*y*(1.0f-c)+c, y*z*(1.0f-c)-x*s, 0.0f,
z*x*(1.0f-c)-y*s, z*y*(1.0f-c)+x*s, z*z*(1.0f-c)+c, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f };
return multiply(rotationMat);
}
Matrix4 & Matrix4::scale( const Vector3 &scaler )
{
float x = scaler.x;
float y = scaler.y;
float z = scaler.z;
Matrix4 scaleMat;
scaleMat.mElements = {
x, 0.0f, 0.0f, 0.0f,
0.0f, y, 0.0f, 0.0f,
0.0f, 0.0f, z, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f };
return multiply(scaleMat);
}
If you use the matrix class like this,
float angle_radians = ....;
Vector3 scaleVec{ 0.2f, 0.2f, 0.2f };
Vector3 transVec{ 0.3f, 0.3f, 0.0f };
Vector3 rotateVec{ 0.0f, 0.0f, 1.0f };
Matrix4 model;
model.rotate( angle_rad, rotateVec );
model.translate( transVec );
model.scale( scaleVec );
then the result would look like this:
The function rotate() isn't performing an actual rotation. Only generating a partial rotation matrix, and overwriting it over the original matrix.
You need to construct a complete one and multiply it to the original matrix.
Matrix4 Matrix4::rotate(const Matrix4& matrix, float angle, const Vector3& axis)
{
if (axis.x == 0 && axis.y == 0 && axis.z == 0)
return matrix;
float r = angle;
float s = sin(r);
float c = cos(r);
float omc = 1.0f - cos(r);
float x = axis.x;
float y = axis.y;
float z = axis.z;
Matrix4 r;
r.mElements[0 + 0 * 4] = c + x * x * omc;
r.mElements[1 + 0 * 4] = x * y * omc - z * s;
r.mElements[2 + 0 * 4] = z * x * omc + y * s;
r.mElements[3 + 0 * 4] = 0;
r.mElements[0 + 1 * 4] = x * y * omc + z * s;
r.mElements[1 + 1 * 4] = c + y * y * omc;
r.mElements[2 + 1 * 4] = z * y * omc - x * s;
r.mElements[3 + 1 * 4] = 0;
r.mElements[0 + 2 * 4] = x * z * omc - y * s;
r.mElements[1 + 2 * 4] = y * z * omc + x * s;
r.mElements[2 + 2 * 4] = c + z * z * omc;
r.mElements[3 + 2 * 4] = 0;
r.mElements[0 + 3 * 4] = 0;
r.mElements[1 + 3 * 4] = 0;
r.mElements[2 + 3 * 4] = 0;
r.mElements[3 + 3 * 4] = 1;
return r * matrix;
}
I'm writing simple renderer in C++. It uses convention similar to OpenGL, but it does not use OpenGL nor DirectX. float3, float4, float4x4 are my own custom structures.
The problem is, when I set the eye somewhere other then 0, 0, 0, I get strange results with triangles where I would not expect to see them.
I guess it's because of wrong matrix multiplication formula, wrong multiplication order, normalization, or wrong formula of lookAt/setPerspective. But I'm stuck at it and I cannot find the mistake.
I will upload some illustrations/screens later, as I don't have access to them now.
I use column-notation for matrices (matrix[column][row]), like OpenGL does.
Here is the matrix multiplication code:
class float4x4 { //[column][row]
float4 columns[4];
public:
float4x4 multiplyBy(float4x4 &b){
float4x4 c = float4x4();
c.columns[0] = float4(
columns[0].x * b.columns[0].x + columns[1].x * b.columns[0].y + columns[2].x * b.columns[0].z + columns[3].x * b.columns[0].w,
columns[0].y * b.columns[0].x + columns[1].y * b.columns[0].y + columns[2].y * b.columns[0].z + columns[3].y * b.columns[0].w,
columns[0].z * b.columns[0].x + columns[1].z * b.columns[0].y + columns[2].z * b.columns[0].z + columns[3].z * b.columns[0].w,
columns[0].w * b.columns[0].x + columns[1].w * b.columns[0].y + columns[2].w * b.columns[0].z + columns[3].w * b.columns[0].w
);
c.columns[1] = float4(
columns[0].x * b.columns[1].x + columns[1].x * b.columns[1].y + columns[2].x * b.columns[1].z + columns[3].x * b.columns[1].w,
columns[0].y * b.columns[1].x + columns[1].y * b.columns[1].y + columns[2].y * b.columns[1].z + columns[3].y * b.columns[1].w,
columns[0].z * b.columns[1].x + columns[1].z * b.columns[1].y + columns[2].z * b.columns[1].z + columns[3].z * b.columns[1].w,
columns[0].w * b.columns[1].x + columns[1].w * b.columns[1].y + columns[2].w * b.columns[1].z + columns[3].w * b.columns[1].w
);
c.columns[2] = float4(
columns[0].x * b.columns[2].x + columns[1].x * b.columns[2].y + columns[2].x * b.columns[2].z + columns[3].x * b.columns[2].w,
columns[0].y * b.columns[2].x + columns[1].y * b.columns[2].y + columns[2].y * b.columns[2].z + columns[3].y * b.columns[2].w,
columns[0].z * b.columns[2].x + columns[1].z * b.columns[2].y + columns[2].z * b.columns[2].z + columns[3].z * b.columns[2].w,
columns[0].w * b.columns[2].x + columns[1].w * b.columns[2].y + columns[2].w * b.columns[2].z + columns[3].w * b.columns[2].w
);
c.columns[3] = float4(
columns[0].x * b.columns[3].x + columns[1].x * b.columns[3].y + columns[2].x * b.columns[3].z + columns[3].x * b.columns[3].w,
columns[0].y * b.columns[3].x + columns[1].y * b.columns[3].y + columns[2].y * b.columns[3].z + columns[3].y * b.columns[3].w,
columns[0].z * b.columns[3].x + columns[1].z * b.columns[3].y + columns[2].z * b.columns[3].z + columns[3].z * b.columns[3].w,
columns[0].w * b.columns[3].x + columns[1].w * b.columns[3].y + columns[2].w * b.columns[3].z + columns[3].w * b.columns[3].w
);
return c;
}
float4 multiplyBy(const float4 &b){
//based on http://stackoverflow.com/questions/25805126/vector-matrix-product-efficiency-issue
float4x4 a = *this; //getTransposed(); ???
float4 result(
dotProduct(a[0], b),
dotProduct(a[1], b),
dotProduct(a[2], b),
dotProduct(a[3], b)
);
return result;
}
inline float4x4 getTransposed() {
float4x4 transposed;
for (unsigned i = 0; i < 4; i++) {
for (unsigned j = 0; j < 4; j++) {
transposed.columns[i][j] = columns[j][i];
}
}
return transposed;
}
};
Where #define dotProduct(a, b) a.getDotProduct(b) and:
inline float getDotProduct(const float4 &anotherVector) const {
return x * anotherVector.x + y * anotherVector.y + z * anotherVector.z + w * anotherVector.w;
}
My VertexProcessor:
class VertexProcessor {
float4x4 obj2world;
float4x4 world2view;
float4x4 view2proj;
float4x4 obj2proj;
public:
inline float3 tr(const float3 & v) { //in object space
float4 r = obj2proj.multiplyBy(float4(v.x, v.y, v.z, 1.0f/*v.w*/));
return float3(r.x / r.w, r.y / r.w, r.z / r.w); //we get vector in unified cube from -1,-1,-1 to 1,1,1
}
inline void transform() {
obj2proj = obj2world.multiplyBy(world2view);
obj2proj = obj2proj.multiplyBy(view2proj);
}
inline void setIdentity() {
obj2world = float4x4(
float4(1.0f, 0.0f, 0.0f, 0.0f),
float4(0.0f, 1.0f, 0.0f, 0.0f),
float4(0.0f, 0.0f, 1.0f, 0.0f),
float4(0.0f, 0.0f, 0.0f, 1.0f)
);
}
inline void setPerspective(float fovy, float aspect, float nearP, float farP) {
fovy *= PI / 360.0f;
float fValue = cos(fovy) / sin(fovy);
view2proj[0] = float4(fValue/aspect, 0.0f, 0.f, 0.0f);
view2proj[1] = float4(0.0f, fValue, 0.0f, 0.0f);
view2proj[2] = float4(0.0f, 0.0f, (farP + nearP) / (nearP - farP), -1.0f);
view2proj[3] = float4(0.0f, 0.0f, 2.0f * farP * nearP / (nearP - farP), 0.0f);
}
inline void setLookat(float3 eye, float3 center, float3 up) {
float3 f = center - eye;
f.normalizeIt();
up.normalizeIt();
float3 s = f.getCrossProduct(up);
float3 u = s.getCrossProduct(f);
world2view[0] = float4(s.x, u.x, -f.x, 0.0f);
world2view[1] = float4(s.y, u.y, -f.y, 0.0f);
world2view[2] = float4(s.z, u.z, -f.z, 0.0f);
world2view[3] = float4(eye/*.getNormalized() ???*/ * -1.0f, 1.0f);
}
inline void multByTranslation(float3 v) {
float4x4 m(
float4(1.0f, 0.0f, 0.0f, 0.0f),
float4(0.0f, 1.0f, 0.0f, 0.0f),
float4(0.0f, 0.0f, 1.0f, 0.0f),
float4(v.x, v.y, v.z, 1.0f)
);
world2view = m.multiplyBy(world2view);
}
inline void multByScale(float3 v) {
float4x4 m(
float4(v.x, 0.0f, 0.0f, 0.0f),
float4(0.0f, v.y, 0.0f, 0.0f),
float4(0.0f, 0.0f, v.z, 0.0f),
float4(0.0f, 0.0f, 0.0f, 1.0f)
);
world2view = m.multiplyBy(world2view);
}
inline void multByRotation(float a, float3 v) {
float s = sin(a*PI / 180.0f), c = cos(a*PI / 180.0f);
v.normalizeIt();
float4x4 m(
float4(v.x*v.x*(1-c)+c, v.y*v.x*(1 - c) + v.z*s, v.x*v.z*(1-c)-v.y*s, 0.0f),
float4(v.x*v.y*(1-c)-v.z*s, v.y*v.y*(1-c)+c, v.y*v.z*(1-c)+v.x*s, 0.0f),
float4(v.x*v.z*(1-c)+v.y*s, v.y*v.z*(1-c)-v.x*s, v.z*v.z*(1-c)+c, 0.0f),
float4(0.0f, 0.0f, 0.0f, 1.0f)
);
world2view = m.multiplyBy(world2view);
}
};
And the Rasterizer:
class Rasterizer final {
Buffer * buffer = nullptr;
inline float toScreenSpaceX(float x) { return (x + 1) * buffer->getWidth() * 0.5f; }
inline float toScreenSpaceY(float y) { return (y + 1) * buffer->getHeight() * 0.5f; }
inline int orient2d(float ax, float ay, float bx, float by, const float2& c) {
return (bx - ax)*(c.y - ay) - (by - ay)*(c.x - ax);
}
public:
Rasterizer(Buffer * buffer) : buffer(buffer) {}
//v - position in screen space ([0, width], [0, height], [-1, -1])
void triangle(
float3 v0, float3 v1, float3 v2,
float3 n0, float3 n1, float3 n2,
float2 uv0, float2 uv1, float2 uv2,
Light * light0, Light * light1,
float3 camera, Texture * texture
) {
v0.x = toScreenSpaceX(v0.x);
v0.y = toScreenSpaceY(v0.y);
v1.x = toScreenSpaceX(v1.x);
v1.y = toScreenSpaceY(v1.y);
v2.x = toScreenSpaceX(v2.x);
v2.y = toScreenSpaceY(v2.y);
//based on: https://fgiesen.wordpress.com/2013/02/08/triangle-rasterization-in-practice/
//compute triangle bounding box
int minX = MIN3(v0.x, v1.x, v2.x);
int minY = MIN3(v0.y, v1.y, v2.y);
int maxX = MAX3(v0.x, v1.x, v2.x);
int maxY = MAX3(v0.y, v1.y, v2.y);
//clip against screen bounds
minX = MAX(minX, 0);
minY = MAX(minY, 0);
maxX = MIN(maxX, buffer->getWidth() - 1);
maxY = MIN(maxY, buffer->getHeight() - 1);
//rasterize
float2 p(0.0f, 0.0f);
for (p.y = minY; p.y <= maxY; p.y++) {
for (p.x = minX; p.x <= maxX; p.x++) {
// Determine barycentric coordinates
//int w0 = orient2d(v1.x, v1.y, v2.x, v2.y, p);
//int w1 = orient2d(v2.x, v2.y, v0.x, v0.y, p);
//int w2 = orient2d(v0.x, v0.y, v1.x, v1.y, p);
float w0 = (v1.y - v2.y)*(p.x - v2.x) + (v2.x - v1.x)*(p.y - v2.y);
w0 /= (v1.y - v2.y)*(v0.x - v2.x) + (v2.x - v1.x)*(v0.y - v2.y);
float w1 = (v2.y - v0.y)*(p.x - v2.x) + (v0.x - v2.x)*(p.y - v2.y);
w1 /= (v2.y - v0.y)*(v1.x - v2.x) + (v0.x - v2.x)*(v1.y - v2.y);
float w2 = 1 - w0 - w1;
// If p is on or inside all edges, render pixel.
if (w0 >= 0 && w1 >= 0 && w2 >= 0) {
float depth = w0 * v0.z + w1 * v1.z + w2 * v2.z;
if (depth < buffer->getDepthForPixel(p.x, p.y)) {
//...
buffer->setPixel(p.x, p.y, diffuse.r, diffuse.g, diffuse.b, ALPHA_VISIBLE, depth);
}
}
}
}
}
};
I strongly believe that Rasterizer itself works well , because when I test it with code (instead of main loop):
float3 v0{ 0, 0, 0.1f };
float3 v1{ 0.5, 0, 0.1f };
float3 v2{ 1, 1, 0.1f };
//Rasterizer test (without VertexProcessor)
rasterizer->triangle(v0, v1, v2, n0, n1, n2, uv0, uv1, uv2, light0, light1, eye, defaultTexture);
I get the right image, with triangle that has one corner at the middle of the screen ([0, 0] in unified space), one at bottom-right corner ([1, 1]) and one at [0.5, 0].
The float3 structure:
class float3 {
public:
union {
struct { float x, y, z; };
struct { float r, g, b; };
float p[3];
};
float3() = delete;
float3(const float3 &other) : x(other.x), y(other.y), z(other.z) {}
float3(float x, float y, float z) : x(x), y(y), z(z) {}
float &operator[](unsigned index){
ERROR_HANDLE(index < 3, L"The float3 index out of bounds (0-2 range, " + C::toWString(index) + L" given).");
return p[index];
}
float getLength() const { return std::abs(sqrt(x*x + y*y + z*z)); }
void normalizeIt();
inline float3 getNormalized() const {
float3 result(*this);
result.normalizeIt();
return result;
}
inline float3 getCrossProduct(const float3 &anotherVector) const {
//based on: http://www.sciencehq.com/physics/vector-product-multiplying-vectors.html
return float3(
y * anotherVector.z - anotherVector.y * z,
z * anotherVector.x - anotherVector.z * x,
x * anotherVector.y - anotherVector.x * y
);
}
inline float getDotProduct(const float3 &anotherVector) const {
//based on: https://www.ltcconline.net/greenl/courses/107/Vectors/DOTCROS.HTM
return x * anotherVector.x + y * anotherVector.y + z * anotherVector.z;
}
...
};
The main loop:
VertexProcessor vp;
DirectionalLight * light0 = new DirectionalLight({ 0.3f, 0.3f, 0.3f }, { 0.0f, -1.0f, 0.0f });
DirectionalLight * light1 = new DirectionalLight({ 0.4f, 0.4f, 0.4f }, { 0.0f, -1.0f, 0.5f });
while(!my_window.is_closed()) {
tgaBuffer.clearDepth(10.0f); //it could be 1.0f but 10.0f won't hurt, we draw pixel if it's depth < actual depth in buffer
tgaBuffer.clearColor(0, 0, 255, ALPHA_VISIBLE);
vp.setPerspective(75.0f, tgaBuffer.getWidth() / tgaBuffer.getHeight(), 10.0f, 2000.0f);
float3 eye = { 10.0f, 10.0f - frameTotal / 10.0f, 10.0f }; //animate eye
vp.setLookat(eye, float3{ 0.0f, 0.0f, 0.0f }.getNormalized(), { 0.0f, 1.0f, 0.0f });
vp.setIdentity();
//we could call e.g. vp.multByRotation(...) here, but we won't to keep it simple
vp.transform();
//bottom
drawTriangle(0, 1, 2);
drawTriangle(2, 3, 0);
drawTriangle(3, 2, 7);
drawTriangle(7, 2, 6);
drawTriangle(5, 1, 0);
drawTriangle(0, 5, 4);
drawTriangle(4, 5, 6);
drawTriangle(6, 7, 4);
frameTotal++;
}
Where drawTriangle(...) stands for:
#define drawTriangle(i0, i1, i2) rasterizer->triangle(vp.tr(v[i0]), vp.tr(v[i1]), vp.tr(v[i2]), v[i0], v[i1], v[i2], n0, n1, n2, uv0, uv1, uv2, light0, light1, eye, defaultTexture);
And here is the initialization of triangles' data:
float3 offset{ 0.0f, 0.0f, 0.0f };
v.push_back(offset + float3{ -10, -10, -10 });
v.push_back(offset + float3{ +10, -10, -10 });
v.push_back(offset + float3{ +10, -10, +10 });
v.push_back(offset + float3{ -10, -10, +10 });
v.push_back(offset + float3{ -10, +10, -10 });
v.push_back(offset + float3{ +10, +10, -10 });
v.push_back(offset + float3{ +10, +10, +10 });
v.push_back(offset + float3{ -10, +10, +10 });
I've created a little c-library for opengl long time ago. It was generally for learning purpose during my studies of computer graphics. I've looked up my sources and my implementation of perspective projection and orientation very much differs.
pbm_Mat4 pbm_mat4_projection_perspective(PBfloat fov, PBfloat ratio, PBfloat near, PBfloat far) {
PBfloat t = near * tanf(fov / 2.0f);
PBfloat b = -t;
PBfloat r = ratio * t, l = ratio * b;
return pbm_mat4_create(pbm_vec4_create(2.0f * near / (r - l), 0, 0, 0),
pbm_vec4_create(0, 2.0f * near / (t - b), 0, 0),
pbm_vec4_create((r + l) / (r - l), (t + b) / (t - b), - (far + near) / (far - near), -1.0f),
pbm_vec4_create(0, 0, -2.0f * far * near / (far - near), 0));
}
pbm_Mat4 pbm_mat4_orientation_lookAt(pbm_Vec3 pos, pbm_Vec3 target, pbm_Vec3 up) {
pbm_Vec3 forward = pbm_vec3_normalize(pbm_vec3_sub(target, pos));
pbm_Vec3 right = pbm_vec3_normalize(pbm_vec3_cross(forward, up));
up = pbm_vec3_normalize(pbm_vec3_cross(right, forward));
forward = pbm_vec3_scalar(forward, -1);
pos = pbm_vec3_scalar(pos, -1);
return pbm_mat4_create(pbm_vec4_create_vec3(right),
pbm_vec4_create_vec3(up),
pbm_vec4_create_vec3(forward),
pbm_vec4_create_vec3_w(pbm_vec3_create(pbm_vec3_dot(right, pos),
pbm_vec3_dot(up, pos),
pbm_vec3_dot(forward, pos)), 1));
}
These methods are tested and you may want to test against them. Iff you want full sources are availabe here. Furthermore you could revisit frustums and projection matrices online. Unfortanetly I can not share the material from my university with you:(
I'm drawing a 10x10 grid of squares at a depth of 0 and trying to highlight the one the mouse is over. I've tried following the tutorial here: http://antongerdelan.net/opengl/raycasting.html
but I don't know if I did it right. I end up with a vector at the end, but I'm not sure what to do with it.
Here's a screenshot of the squares (not sure how it helps..)
http://postimg.org/image/dau330qwt/2
/* Enable attribute index 1 as being used */
glEnableVertexAttribArray(1);
float camera_z = 50;
float camera_x = 0;
float camera_y = 0;
GLuint MatrixID = glGetUniformLocation(program, "MVP");
GLuint ColorID = glGetUniformLocation(program, "input_color");
int mouse_x;
int mouse_y;
while (1) {
int window_width;
int window_height;
SDL_GetWindowSize(win, &window_width, &window_height);
glm::mat4 Projection = glm::perspective(45.0f, ((float)window_width) / window_height, 0.1f, 100.0f);
// printf("Camera at %f %f\n", camera_x, camera_y);
glm::mat4 View = glm::lookAt(glm::vec3(camera_x,camera_y,camera_z), // camera position
glm::vec3(camera_x,camera_y,0), // looking at
glm::vec3(0,1,0)); // up
int map_width = map.width();
int map_height = map.height();
/* Make our background black */
glClearColor(0.0, 0.0, 0.0, 1.0);
glClear(GL_COLOR_BUFFER_BIT);
// go through my 10x10 map and
for (int i = 0; i < map_width; i++) {
for ( int j = 0; j < map_height; j++) {
glm::mat4 Model = glm::translate(glm::mat4(1.0f), glm::vec3(i, j, 0.0f));
glm::mat4 MVP = Projection * View * Model;
glm::vec3 color = random_color();
glUniformMatrix4fv(MatrixID, 1, GL_FALSE, &MVP[0][0]);
glUniform3fv(ColorID, 1, &color[0]);
glDrawArrays(GL_LINE_LOOP, 0, 4);
}
}
/* Swap our buffers to make our changes visible */
SDL_GL_SwapWindow(win);
// printf("Window dimensions %d x %d\n", window_width, window_height);
float normalized_mouse_x = (2.0f * mouse_x) / window_width - 1.0f;
float normalized_mouse_y = 1.0f - (2.0f * mouse_y) / window_height;
printf("Normalized mouse position %f x %f\n", normalized_mouse_x, normalized_mouse_y);
glm::vec3 normalized_mouse_vector = glm::vec3(normalized_mouse_x, normalized_mouse_y, 1.0f);
glm::vec4 ray_clip = glm::vec4 (normalized_mouse_vector.x, normalized_mouse_vector.y, -1.0, 1.0);
glm::vec4 ray_eye = glm::inverse(Projection) * ray_clip;
ray_eye = glm::vec4(ray_eye.xy(), -1.0, 0.0);
glm::vec3 ray_world = (glm::inverse(View) * ray_eye).xyz();
ray_world = glm::normalize(ray_world);
// this prints out values like: World ray: 0.000266, 0.000382, 1.000000
printf("World ray: %f, %f, %f\n", ray_world.x, ray_world.y, ray_world.z);
// l = -(camera_z / ray_world.z)
float l = -(camera_z / ray_world.z);
float mouse_world_x = camera_x + l * ray_world.x;
float mouse_world_y = camera_y + l * ray_world.y;
printf("mouse world %f, %f\n", mouse_world_x, mouse_world_y);
}
Updated with code from BDL's comment. The output I get now is:
Normalized mouse position 0.087500 x 0.145833
World ray: 0.065083, 0.081353, 499.000000
World ray: 0.000130, 0.000163, 1.000000
mouse world -0.006521, -0.008152
I'm expecting the "mouse world" line to have numbers in the 1-10 range, not in the .00x range, though, based on the screenshot above showing a grid of squares with x and y ranging from 0-10.
Thanks for looking.
The intersection between a given ray r, starting at point C (in this case the camera position) with a x/y plane with z=0 can be calculated as follows:
C ... Camera position [cx,cy,cz]
r ... ray direction [rx,ry,rz]
We are searching for the point on the ray that has z=0
C + l*r = [x,y,0]
=>
cz + l*rz = 0
l * rz = -cz
l = -(cz / rz)
The xy-coordinates of the intersection are now:
x = cx + l * rx
y = cy + l * ry
What is left to do is to check in which rectangle this (x,y) coordinates are located.
When I render my app, I'm expecting to see a number of rectangles surrounding the edges of the window. Instead I'm seeing this ..
All objects will be at z == 0.0f. If I dont render my scene using shaders, all objects show fine. So thinking it must be matrix calculation issue?
Anyone know where I might be going wrong with my matrix setups?
matrices is a custom class which contains the 3 matrices ..
public class MatrixUtils {
/* The different matrices */
private Matrix4f modelMatrix = new Matrix4f();
private Matrix4f viewMatrix = new Matrix4f();
private Matrix4f projectionMatrix = new Matrix4f();
public MatrixUtils(){
loadIdentity(modelMatrix);
}
public void loadIdentity(Matrix4f matrix) {
matrix.load(new float[][] {
new float[] { 1, 0, 0, 0 },
new float[] { 0, 1, 0, 0 },
new float[] { 0, 0, 1, 0 },
new float[] { 0, 0, 0, 1 },
});
}
}
Inside my GLEventListener, I setup the matrices with initial values. Called on reshape, setup projection, model and view matrices ..
/* (non-Javadoc)
* #see javax.media.opengl.GLEventListener#reshape(javax.media.opengl.GLAutoDrawable, int, int, int, int)
*/
public void reshape(GLAutoDrawable gLDrawable, int x, int y, int width, int height) {
setupOrtho(width, height, 0.1f, 100.0f);
}
Model and View matrices are set to identity initially. Projection uses an ortho matrix.
private void setupOrtho(float width, float height, float znear, float zfar) {
matrices.loadIdentity(matrices.getModelMatrix());
matrices.loadIdentity(matrices.getViewMatrix());
matrices.setViewMatrix(
setupViewMatrix(
new Vec3(0.0f, 0.0f, 25.0f),
new Vec3(0.0f, 0.0f, 0.0f),
new Vec3(0.0f, 1.0f, 0.0f)));
matrices.setProjectionMatrix(ortho(0, width, 0, height, znear, zfar));
}
Calculate orthographic Projection matrix ..
public Matrix4f ortho(float left, float right, float top, float bottom, float zfar, float znear) {
return new Matrix4f(new float[][] {
new float[] { 2 / (right - left), 0, 0, -((right + left) / (right - left)) },
new float[] { 0, 2 / (top - bottom), 0, -((top + bottom) / (top - bottom)) },
new float[] { 0, 0, -2 / (zfar - znear), -((zfar + znear) / (zfar - znear)) },
new float[] { 0, 0, 0, 1 },
});
}
Calculate View matrix ..
public Matrix4f setupViewMatrix(Vec3 position, Vec3 target, Vec3 up) {
Vec3f f = (new Vec3f(target.sub(position))).normalize();
Vec3f s = (new Vec3f(Vec3.cross(f, up))).normalize();
Vec3f u = (new Vec3f(Vec3.cross(s, f)));
return new Matrix4f(
new float[] {
s.x, s.y, s.z, -Vec3.dot(s, position),
u.x, u.y, u.z, -Vec3.dot(u, position),
-f.x, -f.y, -f.z, Vec3.dot(f, position),
0.0f, 0.0f, 0.0f, 1.0f});
}
Then inside my display() loop, I pass all 3 matrices into each object's draw() function.
public void display(GLAutoDrawable gLDrawable) {
for (CustomObject obj : customObjects.size()){
obj.draw(gl2, matrices, getShaderProgram(), obj.getPosition(), 0.0f);
}
}
This is how my custom objects setup vertexBuffer ..
int COORDS_PER_VERTEX = 3;
int vertexStride = COORDS_PER_VERTEX * 4; // 4 bytes per vertex
ShortBuffer drawListBuffer;
short drawOrder[] = { 0, 1, 2, 0, 2, 3 }; // order to draw vertices
float squareCoordsTemp[] = {
-(getWidth() / 2 * getP2M()), (getHeight() / 2 * getP2M()), 0.0f, // top left
-(getWidth() / 2 * getP2M()), -(getHeight() / 2 * getP2M()), 0.0f, // bottom left
(getWidth() / 2 * getP2M()), -(getHeight() / 2 * getP2M()), 0.0f, // bottom right
(getWidth() / 2 * getP2M()), (getHeight() / 2 * getP2M()), 0.0f }; // top right
squareCoords = squareCoordsTemp;
ByteBuffer bb = ByteBuffer.allocateDirect(squareCoords.length * 4); // # of coordinate values * 4 bytes per float
bb.order(ByteOrder.nativeOrder());
vertexBuffer = bb.asFloatBuffer();
vertexBuffer.put(squareCoords);
vertexBuffer.position(0);
// initialize byte buffer for the draw list
ByteBuffer dlb = ByteBuffer.allocateDirect(drawOrder.length * 2); // # of coordinate values * 2 bytes per short
dlb.order(ByteOrder.nativeOrder());
drawListBuffer = dlb.asShortBuffer();
drawListBuffer.put(drawOrder);
drawListBuffer.position(0);
This is how my CustomObject draws ..
public void draw(final GL2 gl2, MatrixUtils matrices, int shaderProgram, final Vec3 position, final float bodyAngle){
gl2.glUseProgram(shaderProgram);
// enable alpha
gl2.glEnable(GL.GL_BLEND);
gl2.glBlendFunc(GL.GL_SRC_ALPHA, GL.GL_ONE_MINUS_SRC_ALPHA);
// Set color for drawing
setmColorHandle(gl2.glGetUniformLocation(shaderProgram, "vColor"));
gl2.glUniform4fv(getmColorHandle(), 1, getColorArray(), 0);
// get handle to vertex shader's vPosition member
mPositionHandle = gl2.glGetAttribLocation(shaderProgram, "vPosition");
// Enable a handle to the triangle vertices
gl2.glEnableVertexAttribArray(mPositionHandle);
// Prepare the triangle coordinate data
gl2.glVertexAttribPointer(
mPositionHandle, COORDS_PER_VERTEX,
GL2.GL_FLOAT, false,
vertexStride, vertexBuffer);
// get handle to shape's transformation matrix
mProj = gl2.glGetUniformLocation(shaderProgram, "mProj");
mView = gl2.glGetUniformLocation(shaderProgram, "mView");
mModel = gl2.glGetUniformLocation(shaderProgram, "mModel");
// Apply the projection and view transformation
// getP2M() == 60.0f .. pixels to meters for box2d
matrices.loadIdentity(matrices.getModelMatrix());
matrices.setModelMatrix(matrices.translate(matrices.getModelMatrix(), new Vec3(position.x * getP2M(), position.y * getP2M(), position.z * getP2M())));
matrices.setModelMatrix(matrices.rotate(matrices.getModelMatrix(), bodyAngle, 0, 0, 1));
gl2.glUniformMatrix4fv(mProj, 1, true, matrices.getProjectionMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mView, 1, true, matrices.getViewMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mModel, 1, true, matrices.getModelMatrix().getValues(), 0);
// Draw the square
gl2.glDrawElements(
GL2.GL_TRIANGLES, drawOrder.length,
GL2.GL_UNSIGNED_SHORT, drawListBuffer);
// Disable vertex array
gl2.glDisableVertexAttribArray(mPositionHandle);
gl2.glDisable(GL.GL_BLEND);
gl2.glUseProgram(0);
}
Vertex shader ..
#version 120
attribute vec4 vPosition;
uniform mat4 mProj;
uniform mat4 mView;
uniform mat4 mModel;
void main() {
gl_Position = mProj * mView * mModel * vPosition;
}
fragment shader ..
#version 120
uniform vec4 vColor;
void main() {
gl_FragColor = vColor;
}
Definition of Matrix4f ..
public class Matrix4f {
public float[] values;
public Matrix4f() {
this.values = new float[16];
}
/**
* #param values
*/
public Matrix4f(float[] values) {
this.values = values;
}
/**
* #param values
*/
public Matrix4f(float[][] values) {
load(values);
}
/**
* #param values
*/
public void load(float[][] values) {
this.values = new float[] {
values[0][0], values[0][2], values[0][3], values[0][4],
values[1][0], values[1][5], values[1][6], values[1][7],
values[2][0], values[2][8], values[2][9], values[2][10],
values[3][0], values[3][11], values[3][12], values[3][13]
};
}
/**
* Get the values of matrix
*
* #return values
*/
public float[] getValues() {
return this.values;
}
}
Matrix functions ..
public Matrix4f translate(Matrix4f matrix, Vec3 vector) {
Matrix4f transform = new Matrix4f(new float[][] {
new float[] { 1, 0, 0, vector.x },
new float[] { 0, 1, 0, vector.y },
new float[] { 0, 0, 1, vector.z },
new float[] { 0, 0, 0, 1 },
});
return multiply(matrix, transform);
}
public Matrix4f rotate(Matrix4f matrix, float angle, int x, int y, int z) {
Matrix4f transform = new Matrix4f();
float cos = (float) Math.cos(angle);
float sin = (float) Math.sin(angle);
if (z == 1) {
transform.load(new float[][] {
new float[] { cos, -sin, 0, 0 },
new float[] { sin, cos, 0, 0 },
new float[] { 0, 0, 1, 0 },
new float[] { 0, 0, 0, 1 },
});
}
//Add onto the matrix and return the result
return multiply(matrix, transform);
}
public Matrix4f add(Matrix4f matrixA, Matrix4f matrixB) {
Matrix4f matrix = new Matrix4f();
for (int a = 0; a < matrix.values.length; a++){
matrix.values[a] = matrixA.values[a] + matrixB.values[a];
}
return matrix;
}
public Matrix4f multiply(Matrix4f matrixA, Matrix4f matrixB) {
Matrix4f matrix = new Matrix4f(new float[][] {
new float[] {
(matrixA.values[0] * matrixB.values[0]) + (matrixA.values[1] * matrixB.values[4]) + (matrixA.values[2] * matrixB.values[8]) + (matrixA.values[3] * matrixB.values[12]),
(matrixA.values[0] * matrixB.values[1]) + (matrixA.values[1] * matrixB.values[5]) + (matrixA.values[2] * matrixB.values[9]) + (matrixA.values[3] * matrixB.values[13]),
(matrixA.values[0] * matrixB.values[2]) + (matrixA.values[1] * matrixB.values[6]) + (matrixA.values[2] * matrixB.values[10]) + (matrixA.values[3] * matrixB.values[14]),
(matrixA.values[0] * matrixB.values[3]) + (matrixA.values[1] * matrixB.values[7]) + (matrixA.values[2] * matrixB.values[11]) + (matrixA.values[3] * matrixB.values[15])
},
new float[] {
(matrixA.values[4] * matrixB.values[0]) + (matrixA.values[5] * matrixB.values[4]) + (matrixA.values[6] * matrixB.values[8]) + (matrixA.values[7] * matrixB.values[12]),
(matrixA.values[4] * matrixB.values[1]) + (matrixA.values[5] * matrixB.values[5]) + (matrixA.values[6] * matrixB.values[9]) + (matrixA.values[7] * matrixB.values[13]),
(matrixA.values[4] * matrixB.values[2]) + (matrixA.values[5] * matrixB.values[6]) + (matrixA.values[6] * matrixB.values[10]) + (matrixA.values[7] * matrixB.values[14]),
(matrixA.values[4] * matrixB.values[3]) + (matrixA.values[5] * matrixB.values[7]) + (matrixA.values[6] * matrixB.values[11]) + (matrixA.values[7] * matrixB.values[15])
},
new float[] {
(matrixA.values[8] * matrixB.values[0]) + (matrixA.values[9] * matrixB.values[4]) + (matrixA.values[10] * matrixB.values[8]) + (matrixA.values[11] * matrixB.values[12]),
(matrixA.values[8] * matrixB.values[1]) + (matrixA.values[9] * matrixB.values[5]) + (matrixA.values[10] * matrixB.values[9]) + (matrixA.values[11] * matrixB.values[13]),
(matrixA.values[8] * matrixB.values[2]) + (matrixA.values[9] * matrixB.values[6]) + (matrixA.values[10] * matrixB.values[10]) + (matrixA.values[11] * matrixB.values[14]),
(matrixA.values[8] * matrixB.values[3]) + (matrixA.values[9] * matrixB.values[7]) + (matrixA.values[10] * matrixB.values[11]) + (matrixA.values[11] * matrixB.values[15])
},
new float[] {
(matrixA.values[12] * matrixB.values[0]) + (matrixA.values[13] * matrixB.values[4]) + (matrixA.values[14] * matrixB.values[8]) + (matrixA.values[15] * matrixB.values[12]),
(matrixA.values[12] * matrixB.values[1]) + (matrixA.values[13] * matrixB.values[5]) + (matrixA.values[14] * matrixB.values[9]) + (matrixA.values[15] * matrixB.values[13]),
(matrixA.values[12] * matrixB.values[2]) + (matrixA.values[13] * matrixB.values[6]) + (matrixA.values[14] * matrixB.values[10]) + (matrixA.values[15] * matrixB.values[14]),
(matrixA.values[12] * matrixB.values[3]) + (matrixA.values[13] * matrixB.values[7]) + (matrixA.values[14] * matrixB.values[11]) + (matrixA.values[15] * matrixB.values[15])
}
});
return matrix;
}
EDIT:
I've set the uniforms to transpose my matrices, but the squares are still not centered. They should form a square around the screen, instead they show like this and also they dont seem to rotate correctly? ..
EDIT:
I've changed my rotate and translation functions to multiply the matrices, which fixed the rotated issue. My last issue is that I dont seem to be looking at the center of my scene or my objects are not drawn at the center of my field of view. The squares should form a box around the edge of the screen, with a diamond like shape at center of screen.
Is there something wrong with how I position my camera? ..
The View Matrix does not need to be transposed (it's in column-major order) whereas the Projection matrix is in row-major order and does need to be transposed into GL's column-major order.
You can use the appropriate transpose flag as mentioned in the other answers.
The reason you are getting these strange triangles is because the last row of the resulting MVP matrix is not the last row of the identity matrix and thus there is an unintended perspective distortion.
Also, I am not quire sure the view matrix is set up correctly, it should be as follows:
f = normalize(target - position);
s = normalize(f x u);
u = s x f;
_ _
| s.x s.y s.z (-s dot pos) |
| u.x u.y u.z (-s dot pos) |
| -f.x -f.y -f.z (f dot pos) |
| 0 0 0 1 |
_ -
(which needs to be transposed)
It is not clear from you question, but it seems that your Matrix4f is row-major. Generally, there is two ways how to store matrices: row-major and column-major, however there is one important issue:
Historically, IRIS GL used the row-vector convention, then OpenGL (which was based on IRIS GL) switched to column vectors in its specification (to make it match up better with standard mathematical practice) but at the same time switched storage layout from row-major to column-major to make sure that existing IRIS GL code didn’t break. That’s a somewhat unfortunate legacy, since C defaults to row-major storage, so you would normally expect a C library to use that too.
Taken from here
Lets have a look at your view matrix, you have the translation component in it's last row. Assuming that the matrix is row-major, you have build it in transposed way already. When you pass it to the shader with false in glUniformMatrix4fv, due to different layout you eventually get a correct matrix. So you do not need to transpose that matrix. However, you should be aware of different order of matrix multiplication, as far as they are transposed. Transposed matrices should be multiplied as follows (it does not apply for your case, because you multiply matrices in vertex shader):
See this for more details.
On the other side, your projection matrix needs to be transposed. More over, there are some issues with signs of elements, check this.
Your code should be as follows:
public Matrix4f ortho(float left, float right, float top, float bottom, float zfar, float znear) {
return new Matrix4f(new float[][] {
new float[] { 2 / (right - left), 0, 0, -(right + left) / (right - left) },
new float[] { 0, 2 / (top - bottom), 0, -(top + bottom) / (top - bottom) },
new float[] { 0, 0, -2 / (zfar - znear), -(zfar + znear) / (zfar - znear) },
new float[] { 0, 0, 0, 1 },
});
}
Try to pass the projection matrix with true in glUniformMatrix4fv:
gl2.glUniformMatrix4fv(mProj, 1, true, matrices.getProjectionMatrix().getValues(), 0);
I can only guess how your model matrix is created, so it would be better if you make it just identity for the first time.
view matrix is:
f = normalize(pos-target);
u = normalize(cross(up,f));
s = normalize(f,u);
|s.x s.y s.z dot(s,-pos)|
|u.x u.y u.z dot(u,-pos)|
|f.x f.y f.z dot(f,-pos)|
|0 0 0 1 |
in row-major format = {s.x,s.y,s.z,dot(s,-pos),u.x,u.y,u.z,dot(u,-pos),f.x,f.y,f.z,dot(f,-pos),0,0,0,1}
in column-major format = {s.x,u.x,f.x,0,s.y,u.y,f.y,0,s.z,u.z,f.z,0,dot(s,-pos),dot(u,-pos),dot(f,-pos),1}
projection(ortho) matrix:-
|2/(r-l) 0 0 -(r+l)/(r-l)|
|0 2/(t-b) 0 -(t+b)/(t-b) |
|0 0 -2/(f-n) -(f+n)/(f-n)|
|0 0 0 1 |
in row-major = {2/(r-l),0,0,-(r+l)/(r-l),0,2/(t-b),0,-(t+b)/(t-b),0,0,-2/(f-n),-(f+n)/(f-n),0,0,0,1}
in column major = {2/(r-l),0,0,0,0,2/(t-b),0,0,0,0,-2/(f-n),0,-(r+l)/(r-l),-(t+b)/(t-b),-(f+n)/(f-n),1}
use this for column major,
gl2.glUniformMatrix4fv(mProj, 1, false, matrices.getProjectionMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mView, 1, false, matrices.getViewMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mModel, 1, false, matrices.getModelMatrix().getValues(), 0);
and this for row-major,
gl2.glUniformMatrix4fv(mProj, 1, true, matrices.getProjectionMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mView, 1, true, matrices.getViewMatrix().getValues(), 0);
gl2.glUniformMatrix4fv(mModel, 1, true, matrices.getModelMatrix().getValues(), 0);
pick either row or column major matrices and stick to it.
if that does not work then try copying your vertex data to opengl yourself with glGenBuffer()/glBindBuffer()/glBufferData etc...
r
eturn new Matrix4f(
new float[] {
s.x, s.y, s.z, -Vec3.dot(s, position),
u.x, u.y, u.z, -Vec3.dot(s, position),
-f.x, -f.y, -f.z, Vec3.dot(f, position),
0.0f, 0.0f, 0.0f, 1.0f});
}
should be,
return new Matrix4f(
new float[] {
s.x, s.y, s.z, -Vec3.dot(s, position),
u.x, u.y, u.z, -Vec3.dot(u, position),
-f.x, -f.y, -f.z, Vec3.dot(f, position),
0.0f, 0.0f, 0.0f, 1.0f});
}
also check your vertex shader, you have attribute vec4 vPosition, but you are passing in vec3 data.
i think it should be attribute vec3 vPosition and do,
gl_Position = mProj * mView * mModel * vec4(vPosition,1);
EDIT:
your vertex buffer is:-
int COORDS_PER_VERTEX = 3;
int vertexStride = COORDS_PER_VERTEX * 4; // 4 bytes per vertex
which are vec3's.
EDIT 2.
can i see your customObjects data that draw uses such as position and bodyangle. could you also print out the proj, view and model matrices before they are passed to your shader program.
I have a ray tracer (from www.scratchapixel.com) that I use to write a image to memory that I then display at once using Opengl (glut). I use the width and height and divide the screen to get a Opengl point for every pixels. It kinda works.
My problem is that my width has to be between 500 and 799. It cannot be <= 499 of >= 800, witch doesn't make sense to me. The image becomes skew. I have tried it on 2 computers with the same result.
799x480
800x480
Here's the full code:
#define _USE_MATH_DEFINES
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <fstream>
#include <vector>
#include <iostream>
#include <cassert>
// OpenGl
#include "GL/glut.h"
GLuint width = 799, height = 480;
GLdouble width_step = 2.0f / width, height_step = 2.0f / height;
const int MAX_RAY_DEPTH = 3;
const double INFINITY = HUGE_VAL;
template<typename T>
class Vec3
{
public:
T x, y, z;
// Vector constructors.
Vec3() : x(T(0)), y(T(0)), z(T(0)) {}
Vec3(T xx) : x(xx), y(xx), z(xx) {}
Vec3(T xx, T yy, T zz) : x(xx), y(yy), z(zz) {}
// Vector normalisation.
Vec3& normalize()
{
T nor = x * x + y * y + z * z;
if (nor > 1) {
T invNor = 1 / sqrt(nor);
x *= invNor, y *= invNor, z *= invNor;
}
return *this;
}
// Vector operators.
Vec3<T> operator * (const T &f) const { return Vec3<T>(x * f, y * f, z * f); }
Vec3<T> operator * (const Vec3<T> &v) const { return Vec3<T>(x * v.x, y * v.y, z * v.z); }
T dot(const Vec3<T> &v) const { return x * v.x + y * v.y + z * v.z; }
Vec3<T> operator - (const Vec3<T> &v) const { return Vec3<T>(x - v.x, y - v.y, z - v.z); }
Vec3<T> operator + (const Vec3<T> &v) const { return Vec3<T>(x + v.x, y + v.y, z + v.z); }
Vec3<T>& operator += (const Vec3<T> &v) { x += v.x, y += v.y, z += v.z; return *this; }
Vec3<T>& operator *= (const Vec3<T> &v) { x *= v.x, y *= v.y, z *= v.z; return *this; }
Vec3<T> operator - () const { return Vec3<T>(-x, -y, -z); }
};
template<typename T>
class Sphere
{
public:
// Sphere variables.
Vec3<T> center; /// position of the sphere
T radius, radius2; /// sphere radius and radius^2
Vec3<T> surfaceColor, emissionColor; /// surface color and emission (light)
T transparency, reflection; /// surface transparency and reflectivity
// Sphere constructor.
// position(c), radius(r), surface color(sc), reflectivity(refl), transparency(transp), emission color(ec)
Sphere(const Vec3<T> &c, const T &r, const Vec3<T> &sc,
const T &refl = 0, const T &transp = 0, const Vec3<T> &ec = 0) :
center(c), radius(r), surfaceColor(sc), reflection(refl),
transparency(transp), emissionColor(ec), radius2(r * r)
{}
// compute a ray-sphere intersection using the geometric solution
bool intersect(const Vec3<T> &rayorig, const Vec3<T> &raydir, T *t0 = NULL, T *t1 = NULL) const
{
// we start with a vector (l) from the ray origin (rayorig) to the center of the curent sphere.
Vec3<T> l = center - rayorig;
// tca is a vector length in the direction of the normalise raydir.
// its length is streched using dot until it forms a perfect right angle triangle with the l vector.
T tca = l.dot(raydir);
// if tca is < 0, the raydir is going in the opposite direction. No need to go further. Return false.
if (tca < 0) return false;
// if we keep on into the code, it's because the raydir may still hit the sphere.
// l.dot(l) gives us the l vector length to the power of 2. Then we use Pythagoras' theorem.
// remove the length tca to the power of two (tca * tca) and we get a distance from the center of the sphere to the power of 2 (d2).
T d2 = l.dot(l) - (tca * tca);
// if this distance to the center (d2) is greater than the radius to the power of 2 (radius2), the raydir direction is missing the sphere.
// No need to go further. Return false.
if (d2 > radius2) return false;
// Pythagoras' theorem again: radius2 is the hypotenuse and d2 is one of the side. Substraction gives the third side to the power of 2.
// Using sqrt, we obtain the length thc. thc is how deep tca goes into the sphere.
T thc = sqrt(radius2 - d2);
if (t0 != NULL && t1 != NULL) {
// remove thc to tca and you get the length from the ray origin to the surface hit point of the sphere.
*t0 = tca - thc;
// add thc to tca and you get the length from the ray origin to the surface hit point of the back side of the sphere.
*t1 = tca + thc;
}
// There is a intersection with a sphere, t0 and t1 have surface distances values. Return true.
return true;
}
};
std::vector<Sphere<double> *> spheres;
// function to mix 2 T varables.
template<typename T>
T mix(const T &a, const T &b, const T &mix)
{
return b * mix + a * (T(1) - mix);
}
// This is the main trace function. It takes a ray as argument (defined by its origin
// and direction). We test if this ray intersects any of the geometry in the scene.
// If the ray intersects an object, we compute the intersection point, the normal
// at the intersection point, and shade this point using this information.
// Shading depends on the surface property (is it transparent, reflective, diffuse).
// The function returns a color for the ray. If the ray intersects an object, it
// returns the color of the object at the intersection point, otherwise it returns
// the background color.
template<typename T>
Vec3<T> trace(const Vec3<T> &rayorig, const Vec3<T> &raydir,
const std::vector<Sphere<T> *> &spheres, const int &depth)
{
T tnear = INFINITY;
const Sphere<T> *sphere = NULL;
// Try to find intersection of this raydir with the spheres in the scene
for (unsigned i = 0; i < spheres.size(); ++i) {
T t0 = INFINITY, t1 = INFINITY;
if (spheres[i]->intersect(rayorig, raydir, &t0, &t1)) {
// is the rayorig inside the sphere (t0 < 0)? If so, use the second hit (t0 = t1)
if (t0 < 0) t0 = t1;
// tnear is the last sphere intersection (or infinity). Is t0 in front of tnear?
if (t0 < tnear) {
// if so, update tnear to this closer t0 and update the closest sphere
tnear = t0;
sphere = spheres[i];
}
}
}
// At this moment in the program, we have the closest sphere (sphere) and the closest hit position (tnear)
// For this pixel, if there's no intersection with a sphere, return a Vec3 with the background color.
if (!sphere) return Vec3<T>(.5); // Grey background color.
// if we keep on with the code, it is because we had an intersection with at least one sphere.
Vec3<T> surfaceColor = 0; // initialisation of the color of the ray/surface of the object intersected by the ray.
Vec3<T> phit = rayorig + (raydir * tnear); // point of intersection.
Vec3<T> nhit = phit - sphere->center; // normal at the intersection point.
// if the normal and the view direction are not opposite to each other,
// reverse the normal direction.
if (raydir.dot(nhit) > 0) nhit = -nhit;
nhit.normalize(); // normalize normal direction
// The angle between raydir and the normal at point hit (not used).
//T s_angle = acos(raydir.dot(nhit)) / ( sqrt(raydir.dot(raydir)) * sqrt(nhit.dot(nhit)));
//T s_incidence = sin(s_angle);
T bias = 1e-5; // add some bias to the point from which we will be tracing
// Do we have transparency or reflection?
if ((sphere->transparency > 0 || sphere->reflection > 0) && depth < MAX_RAY_DEPTH) {
T IdotN = raydir.dot(nhit); // raydir.normal
// I and N are not pointing in the same direction, so take the invert.
T facingratio = std::max(T(0), -IdotN);
// change the mix value between reflection and refraction to tweak the effect (fresnel effect)
T fresneleffect = mix<T>(pow(1 - facingratio, 3), 1, 0.1);
// compute reflection direction (not need to normalize because all vectors
// are already normalized)
Vec3<T> refldir = raydir - nhit * 2 * raydir.dot(nhit);
Vec3<T> reflection = trace(phit + (nhit * bias), refldir, spheres, depth + 1);
Vec3<T> refraction = 0;
// if the sphere is also transparent compute refraction ray (transmission)
if (sphere->transparency) {
T ior = 1.2, eta = 1 / ior;
T k = 1 - eta * eta * (1 - IdotN * IdotN);
Vec3<T> refrdir = raydir * eta - nhit * (eta * IdotN + sqrt(k));
refraction = trace(phit - nhit * bias, refrdir, spheres, depth + 1);
}
// the result is a mix of reflection and refraction (if the sphere is transparent)
surfaceColor = (reflection * fresneleffect + refraction * (1 - fresneleffect) * sphere->transparency) * sphere->surfaceColor;
}
else {
// it's a diffuse object, no need to raytrace any further
// Look at all sphere to find lights
double shadow = 1.0;
for (unsigned i = 0; i < spheres.size(); ++i) {
if (spheres[i]->emissionColor.x > 0) {
// this is a light
Vec3<T> transmission = 1.0;
Vec3<T> lightDirection = spheres[i]->center - phit;
lightDirection.normalize();
T light_angle = (acos(raydir.dot(lightDirection)) / ( sqrt(raydir.dot(raydir)) * sqrt(lightDirection.dot(lightDirection))));
T light_incidence = sin(light_angle);
for (unsigned j = 0; j < spheres.size(); ++j) {
if (i != j) {
T t0, t1;
// Does the ray from point hit to the light intersect an object?
// If so, calculate the shadow.
if (spheres[j]->intersect(phit + (nhit * bias), lightDirection, &t0, &t1)) {
shadow = std::max(0.0, shadow - (1.0 - spheres[j]->transparency));
transmission = transmission * spheres[j]->surfaceColor * shadow;
//break;
}
}
}
// For each light found, we add light transmission to the pixel.
surfaceColor += sphere->surfaceColor * transmission *
std::max(T(0), nhit.dot(lightDirection)) * spheres[i]->emissionColor;
}
}
}
return surfaceColor + sphere->emissionColor;
}
// Main rendering function. We compute a camera ray for each pixel of the image,
// trace it and return a color. If the ray hits a sphere, we return the color of the
// sphere at the intersection point, else we return the background color.
Vec3<double> *image = new Vec3<double>[width * height];
static Vec3<double> cam_pos = Vec3<double>(0);
template<typename T>
void render(const std::vector<Sphere<T> *> &spheres)
{
Vec3<T> *pixel = image;
T invWidth = 1 / T(width), invHeight = 1 / T(height);
T fov = 30, aspectratio = T(width) / T(height);
T angle = tan(M_PI * 0.5 * fov / T(180));
// Trace rays
for (GLuint y = 0; y < height; ++y) {
for (GLuint x = 0; x < width; ++x, ++pixel) {
T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
Vec3<T> raydir(xx, yy, -1);
raydir.normalize();
*pixel = trace(cam_pos, raydir, spheres, 0);
}
}
}
//********************************** OPEN GL ***********************************************
void init(void)
{
/* Select clearing (background) color */
glClearColor(0.0, 0.0, 0.0, 0.0);
glShadeModel(GL_FLAT);
/* Initialize viewing values */
//glMatrixMode(GL_PROJECTION);
gluOrtho2D(0,width,0,height);
}
void advanceDisplay(void)
{
cam_pos.z = cam_pos.z - 2;
glutPostRedisplay();
}
void backDisplay(void)
{
cam_pos.z = cam_pos.z + 2;
glutPostRedisplay();
}
void resetDisplay(void)
{
Vec3<double> new_cam_pos;
new_cam_pos = cam_pos;
cam_pos = new_cam_pos;
glutPostRedisplay();
}
void reshape(int w, int h)
{
glLoadIdentity();
gluOrtho2D(0,width,0,height);
glLoadIdentity();
}
void mouse(int button, int state, int x, int y)
{
switch (button)
{
case GLUT_LEFT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(advanceDisplay);
}
break;
case GLUT_MIDDLE_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(resetDisplay);
}
break;
case GLUT_RIGHT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(backDisplay);
}
break;
}
}
void display(void)
{
int i;
float x, y;
/* clear all pixels */
glClear(GL_COLOR_BUFFER_BIT);
glPushMatrix();
render<double>(spheres); // Creates the image and put it to memory in image[].
i=0;
glBegin(GL_POINTS);
for(y=1.0f;y>-1.0;y=y-height_step)
{
for(x=1.0f;x>-1.0;x=x-width_step)
{
glColor3f((std::min(double(1), image[i].x)),
(std::min(double(1), image[i].y)),
(std::min(double(1), image[i].z)));
glVertex2f(x, y);
if(i < width*height)
{
i = i + 1;
}
}
}
glEnd();
glPopMatrix();
glutSwapBuffers();
}
int main(int argc, char **argv)
{
// position, radius, surface color, reflectivity, transparency, emission color
spheres.push_back(new Sphere<double>(Vec3<double>(0, -10004, -20), 10000, Vec3<double>(0.2), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(3, 0, -15), 2, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(1, -1, -18), 1, Vec3<double>(1.0, 1.0, 1.0), 0.9, 0.9));
spheres.push_back(new Sphere<double>(Vec3<double>(-2, 2, -15), 2, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 3, -18), 1, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 0, -25), 1, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(-1, 1, -25), 2, Vec3<double>(1.0, 1.0, 1.0), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(2, 2, -25), 1, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(5, 3, -25), 2, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
// light
spheres.push_back(new Sphere<double>(Vec3<double>(-10, 20, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(3)));
spheres.push_back(new Sphere<double>(Vec3<double>(0, 10, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(1)));
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
glutInitWindowSize(width, height);
glutInitWindowPosition(10,10);
glutCreateWindow(argv[0]);
init();
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutMouseFunc(mouse);
glutMainLoop();
delete [] image;
while (!spheres.empty()) {
Sphere<double> *sph = spheres.back();
spheres.pop_back();
delete sph;
}
return 0;
}
This is where the image is written to memory:
Vec3<double> *image = new Vec3<double>[width * height];
static Vec3<double> cam_pos = Vec3<double>(0);
template<typename T>
void render(const std::vector<Sphere<T> *> &spheres)
{
Vec3<T> *pixel = image;
T invWidth = 1 / T(width), invHeight = 1 / T(height);
T fov = 30, aspectratio = T(width) / T(height);
T angle = tan(M_PI * 0.5 * fov / T(180));
// Trace rays
for (GLuint y = 0; y < height; ++y) {
for (GLuint x = 0; x < width; ++x, ++pixel) {
T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
Vec3<T> raydir(xx, yy, -1);
raydir.normalize();
*pixel = trace(cam_pos, raydir, spheres, 0);
}
}
}
This is where I read it back and write it to each point of Opengl:
void display(void)
{
int i;
float x, y;
/* clear all pixels */
glClear(GL_COLOR_BUFFER_BIT);
glPushMatrix();
render<double>(spheres); // Creates the image and put it to memory in image[].
i=0;
glBegin(GL_POINTS);
for(y=1.0f;y>-1.0;y=y-height_step)
{
for(x=1.0f;x>-1.0;x=x-width_step)
{
glColor3f((std::min(double(1), image[i].x)),
(std::min(double(1), image[i].y)),
(std::min(double(1), image[i].z)));
glVertex2f(x, y);
if(i < width*height)
{
i = i + 1;
}
}
}
glEnd();
glPopMatrix();
glutSwapBuffers();
}
I have no idea what is causing this. Is it a bad design? An Opengl display mode? I don't know.
Is it a bad design?
Yes! Upload your rendered scene to a texture and then render a quad with it:
// g++ -O3 main.cpp -lglut -lGL -lGLU
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <fstream>
#include <vector>
#include <iostream>
#include <cassert>
// OpenGl
#include "GL/glut.h"
GLuint width = 800, height = 480;
GLdouble width_step = 2.0f / width;
GLdouble height_step = 2.0f / height;
const int MAX_RAY_DEPTH = 3;
template<typename T>
class Vec3
{
public:
T x, y, z;
// Vector constructors.
Vec3() : x(T(0)), y(T(0)), z(T(0)) {}
Vec3(T xx) : x(xx), y(xx), z(xx) {}
Vec3(T xx, T yy, T zz) : x(xx), y(yy), z(zz) {}
// Vector normalisation.
Vec3& normalize()
{
T nor = x * x + y * y + z * z;
if (nor > 1) {
T invNor = 1 / sqrt(nor);
x *= invNor, y *= invNor, z *= invNor;
}
return *this;
}
// Vector operators.
Vec3<T> operator * (const T &f) const { return Vec3<T>(x * f, y * f, z * f); }
Vec3<T> operator * (const Vec3<T> &v) const { return Vec3<T>(x * v.x, y * v.y, z * v.z); }
T dot(const Vec3<T> &v) const { return x * v.x + y * v.y + z * v.z; }
Vec3<T> operator - (const Vec3<T> &v) const { return Vec3<T>(x - v.x, y - v.y, z - v.z); }
Vec3<T> operator + (const Vec3<T> &v) const { return Vec3<T>(x + v.x, y + v.y, z + v.z); }
Vec3<T>& operator += (const Vec3<T> &v) { x += v.x, y += v.y, z += v.z; return *this; }
Vec3<T>& operator *= (const Vec3<T> &v) { x *= v.x, y *= v.y, z *= v.z; return *this; }
Vec3<T> operator - () const { return Vec3<T>(-x, -y, -z); }
};
template<typename T>
class Sphere
{
public:
// Sphere variables.
Vec3<T> center; /// position of the sphere
T radius, radius2; /// sphere radius and radius^2
Vec3<T> surfaceColor, emissionColor; /// surface color and emission (light)
T transparency, reflection; /// surface transparency and reflectivity
// Sphere constructor.
// position(c), radius(r), surface color(sc), reflectivity(refl), transparency(transp), emission color(ec)
Sphere(const Vec3<T> &c, const T &r, const Vec3<T> &sc,
const T &refl = 0, const T &transp = 0, const Vec3<T> &ec = 0) :
center(c), radius(r), surfaceColor(sc), reflection(refl),
transparency(transp), emissionColor(ec), radius2(r * r)
{}
// compute a ray-sphere intersection using the geometric solution
bool intersect(const Vec3<T> &rayorig, const Vec3<T> &raydir, T *t0 = NULL, T *t1 = NULL) const
{
// we start with a vector (l) from the ray origin (rayorig) to the center of the curent sphere.
Vec3<T> l = center - rayorig;
// tca is a vector length in the direction of the normalise raydir.
// its length is streched using dot until it forms a perfect right angle triangle with the l vector.
T tca = l.dot(raydir);
// if tca is < 0, the raydir is going in the opposite direction. No need to go further. Return false.
if (tca < 0) return false;
// if we keep on into the code, it's because the raydir may still hit the sphere.
// l.dot(l) gives us the l vector length to the power of 2. Then we use Pythagoras' theorem.
// remove the length tca to the power of two (tca * tca) and we get a distance from the center of the sphere to the power of 2 (d2).
T d2 = l.dot(l) - (tca * tca);
// if this distance to the center (d2) is greater than the radius to the power of 2 (radius2), the raydir direction is missing the sphere.
// No need to go further. Return false.
if (d2 > radius2) return false;
// Pythagoras' theorem again: radius2 is the hypotenuse and d2 is one of the side. Substraction gives the third side to the power of 2.
// Using sqrt, we obtain the length thc. thc is how deep tca goes into the sphere.
T thc = sqrt(radius2 - d2);
if (t0 != NULL && t1 != NULL) {
// remove thc to tca and you get the length from the ray origin to the surface hit point of the sphere.
*t0 = tca - thc;
// add thc to tca and you get the length from the ray origin to the surface hit point of the back side of the sphere.
*t1 = tca + thc;
}
// There is a intersection with a sphere, t0 and t1 have surface distances values. Return true.
return true;
}
};
std::vector<Sphere<double> *> spheres;
// function to mix 2 T varables.
template<typename T>
T mix(const T &a, const T &b, const T &mix)
{
return b * mix + a * (T(1) - mix);
}
// This is the main trace function. It takes a ray as argument (defined by its origin
// and direction). We test if this ray intersects any of the geometry in the scene.
// If the ray intersects an object, we compute the intersection point, the normal
// at the intersection point, and shade this point using this information.
// Shading depends on the surface property (is it transparent, reflective, diffuse).
// The function returns a color for the ray. If the ray intersects an object, it
// returns the color of the object at the intersection point, otherwise it returns
// the background color.
template<typename T>
Vec3<T> trace(const Vec3<T> &rayorig, const Vec3<T> &raydir,
const std::vector<Sphere<T> *> &spheres, const int &depth)
{
T tnear = INFINITY;
const Sphere<T> *sphere = NULL;
// Try to find intersection of this raydir with the spheres in the scene
for (unsigned i = 0; i < spheres.size(); ++i) {
T t0 = INFINITY, t1 = INFINITY;
if (spheres[i]->intersect(rayorig, raydir, &t0, &t1)) {
// is the rayorig inside the sphere (t0 < 0)? If so, use the second hit (t0 = t1)
if (t0 < 0) t0 = t1;
// tnear is the last sphere intersection (or infinity). Is t0 in front of tnear?
if (t0 < tnear) {
// if so, update tnear to this closer t0 and update the closest sphere
tnear = t0;
sphere = spheres[i];
}
}
}
// At this moment in the program, we have the closest sphere (sphere) and the closest hit position (tnear)
// For this pixel, if there's no intersection with a sphere, return a Vec3 with the background color.
if (!sphere) return Vec3<T>(.5); // Grey background color.
// if we keep on with the code, it is because we had an intersection with at least one sphere.
Vec3<T> surfaceColor = 0; // initialisation of the color of the ray/surface of the object intersected by the ray.
Vec3<T> phit = rayorig + (raydir * tnear); // point of intersection.
Vec3<T> nhit = phit - sphere->center; // normal at the intersection point.
// if the normal and the view direction are not opposite to each other,
// reverse the normal direction.
if (raydir.dot(nhit) > 0) nhit = -nhit;
nhit.normalize(); // normalize normal direction
// The angle between raydir and the normal at point hit (not used).
//T s_angle = acos(raydir.dot(nhit)) / ( sqrt(raydir.dot(raydir)) * sqrt(nhit.dot(nhit)));
//T s_incidence = sin(s_angle);
T bias = 1e-5; // add some bias to the point from which we will be tracing
// Do we have transparency or reflection?
if ((sphere->transparency > 0 || sphere->reflection > 0) && depth < MAX_RAY_DEPTH) {
T IdotN = raydir.dot(nhit); // raydir.normal
// I and N are not pointing in the same direction, so take the invert.
T facingratio = std::max(T(0), -IdotN);
// change the mix value between reflection and refraction to tweak the effect (fresnel effect)
T fresneleffect = mix<T>(pow(1 - facingratio, 3), 1, 0.1);
// compute reflection direction (not need to normalize because all vectors
// are already normalized)
Vec3<T> refldir = raydir - nhit * 2 * raydir.dot(nhit);
Vec3<T> reflection = trace(phit + (nhit * bias), refldir, spheres, depth + 1);
Vec3<T> refraction = 0;
// if the sphere is also transparent compute refraction ray (transmission)
if (sphere->transparency) {
T ior = 1.2, eta = 1 / ior;
T k = 1 - eta * eta * (1 - IdotN * IdotN);
Vec3<T> refrdir = raydir * eta - nhit * (eta * IdotN + sqrt(k));
refraction = trace(phit - nhit * bias, refrdir, spheres, depth + 1);
}
// the result is a mix of reflection and refraction (if the sphere is transparent)
surfaceColor = (reflection * fresneleffect + refraction * (1 - fresneleffect) * sphere->transparency) * sphere->surfaceColor;
}
else {
// it's a diffuse object, no need to raytrace any further
// Look at all sphere to find lights
double shadow = 1.0;
for (unsigned i = 0; i < spheres.size(); ++i) {
if (spheres[i]->emissionColor.x > 0) {
// this is a light
Vec3<T> transmission = 1.0;
Vec3<T> lightDirection = spheres[i]->center - phit;
lightDirection.normalize();
T light_angle = (acos(raydir.dot(lightDirection)) / ( sqrt(raydir.dot(raydir)) * sqrt(lightDirection.dot(lightDirection))));
T light_incidence = sin(light_angle);
for (unsigned j = 0; j < spheres.size(); ++j) {
if (i != j) {
T t0, t1;
// Does the ray from point hit to the light intersect an object?
// If so, calculate the shadow.
if (spheres[j]->intersect(phit + (nhit * bias), lightDirection, &t0, &t1)) {
shadow = std::max(0.0, shadow - (1.0 - spheres[j]->transparency));
transmission = transmission * spheres[j]->surfaceColor * shadow;
//break;
}
}
}
// For each light found, we add light transmission to the pixel.
surfaceColor += sphere->surfaceColor * transmission *
std::max(T(0), nhit.dot(lightDirection)) * spheres[i]->emissionColor;
}
}
}
return surfaceColor + sphere->emissionColor;
}
// Main rendering function. We compute a camera ray for each pixel of the image,
// trace it and return a color. If the ray hits a sphere, we return the color of the
// sphere at the intersection point, else we return the background color.
Vec3<double> *image = new Vec3<double>[width * height];
static Vec3<double> cam_pos = Vec3<double>(0);
template<typename T>
void render(const std::vector<Sphere<T> *> &spheres)
{
Vec3<T> *pixel = image;
T invWidth = 1 / T(width), invHeight = 1 / T(height);
T fov = 30, aspectratio = T(width) / T(height);
T angle = tan(M_PI * 0.5 * fov / T(180));
// Trace rays
for (GLuint y = 0; y < height; ++y) {
for (GLuint x = 0; x < width; ++x, ++pixel) {
T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
Vec3<T> raydir(xx, yy, -1);
raydir.normalize();
*pixel = trace(cam_pos, raydir, spheres, 0);
}
}
}
//********************************** OPEN GL ***********************************************
void advanceDisplay(void)
{
cam_pos.z = cam_pos.z - 2;
glutPostRedisplay();
}
void backDisplay(void)
{
cam_pos.z = cam_pos.z + 2;
glutPostRedisplay();
}
void resetDisplay(void)
{
Vec3<double> new_cam_pos;
new_cam_pos = cam_pos;
cam_pos = new_cam_pos;
glutPostRedisplay();
}
void mouse(int button, int state, int x, int y)
{
switch (button)
{
case GLUT_LEFT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(advanceDisplay);
}
break;
case GLUT_MIDDLE_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(resetDisplay);
}
break;
case GLUT_RIGHT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(backDisplay);
}
break;
}
}
GLuint tex = 0;
void display(void)
{
int i;
float x, y;
render<double>(spheres); // Creates the image and put it to memory in image[].
std::vector< unsigned char > buf;
buf.reserve( width * height * 3 );
for( size_t y = 0; y < height; ++y )
{
for( size_t x = 0; x < width; ++x )
{
// flip vertically (height-y) because the OpenGL texture origin is in the lower-left corner
// flip horizontally (width-x) because...the original code did so
size_t i = (height-y) * width + (width-x);
buf.push_back( (unsigned char)( std::min(double(1), image[i].x) * 255.0 ) );
buf.push_back( (unsigned char)( std::min(double(1), image[i].y) * 255.0 ) );
buf.push_back( (unsigned char)( std::min(double(1), image[i].z) * 255.0 ) );
}
}
/* clear all pixels */
glClearColor(0.0, 0.0, 0.0, 0.0);
glClear(GL_COLOR_BUFFER_BIT);
glMatrixMode( GL_PROJECTION );
glLoadIdentity();
glMatrixMode( GL_MODELVIEW );
glLoadIdentity();
glEnable( GL_TEXTURE_2D );
glBindTexture( GL_TEXTURE_2D, tex );
glTexSubImage2D
(
GL_TEXTURE_2D, 0,
0, 0,
width, height,
GL_RGB,
GL_UNSIGNED_BYTE,
&buf[0]
);
glBegin( GL_QUADS );
glTexCoord2i( 0, 0 );
glVertex2i( -1, -1 );
glTexCoord2i( 1, 0 );
glVertex2i( 1, -1 );
glTexCoord2i( 1, 1 );
glVertex2i( 1, 1 );
glTexCoord2i( 0, 1 );
glVertex2i( -1, 1 );
glEnd();
glutSwapBuffers();
}
int main(int argc, char **argv)
{
// position, radius, surface color, reflectivity, transparency, emission color
spheres.push_back(new Sphere<double>(Vec3<double>(0, -10004, -20), 10000, Vec3<double>(0.2), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(3, 0, -15), 2, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(1, -1, -18), 1, Vec3<double>(1.0, 1.0, 1.0), 0.9, 0.9));
spheres.push_back(new Sphere<double>(Vec3<double>(-2, 2, -15), 2, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 3, -18), 1, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 0, -25), 1, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(-1, 1, -25), 2, Vec3<double>(1.0, 1.0, 1.0), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(2, 2, -25), 1, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(5, 3, -25), 2, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
// light
spheres.push_back(new Sphere<double>(Vec3<double>(-10, 20, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(3)));
spheres.push_back(new Sphere<double>(Vec3<double>(0, 10, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(1)));
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
glutInitWindowSize(width, height);
glutInitWindowPosition(10,10);
glutCreateWindow(argv[0]);
glutDisplayFunc(display);
glutMouseFunc(mouse);
glGenTextures( 1, &tex );
glBindTexture( GL_TEXTURE_2D, tex );
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE );
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE );
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR );
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR );
glPixelStorei( GL_UNPACK_ALIGNMENT, 1 );
glTexImage2D( GL_TEXTURE_2D, 0, 3, width, height, 0, GL_RGB, GL_UNSIGNED_BYTE, NULL );
glutMainLoop();
delete [] image;
while (!spheres.empty()) {
Sphere<double> *sph = spheres.back();
spheres.pop_back();
delete sph;
}
return 0;
}
How to load and display images is also explained on www.scratchapixel.com. Strange you didn't see this lesson:
http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-5-colors-and-digital-images/source-code/
It's all in there and they explain you how to display images using GL textures indeed.