I'm trying to create a perspective projection matrix for OpenGL. I know how to do it with a float[16] but for consistencies sake I'd like to use an Eigen matrix.
The formula is:
[ xScale 0 0 0 ]
P = [ 0 yScale 0 0 ]
[ 0 0 -(zFar+zNear)/(zFar-zNear) -2*zNear*zFar/(zFar-zNear) ]
[ 0 0 -1 0 ]
Where:
yScale = cot(fovY/2)
xScale = yScale/aspectRatio
Since the formula is column-major and c-arrays are defined row-major, you would define a float[16] matrix with:
float P[16] = {
xScale, 0, 0, 0,
0, yScale, 0, 0,
0, 0, -(zFar+zNear)/(zFar-zNear), -1
0, 0, -2*zNear*zFar/(zFar-zNear), 0
};
So how exactly would I create a matrix like this with Eigen? Would I use an Eigen::Affine3f or a Eigen::Matrix4f? Looking at the documentation, it's not apparent to me how to set individual cell values.
In your case, the simplest is to use the comma initializer syntax:
Eigen::Matrix4f pmat;
pmat << xScale, 0, 0, 0,
0, yScale, 0, 0,
0, 0, -(zFar+zNear)/(zFar-zNear), -1,
0, 0, -2*zNear*zFar/(zFar-zNear), 0;
Setting individual cell values can be done simply with a paren, e.g. Matrix(0,0) = xScale; .
Related
This is my perspective projection matrix code
inline m4
Projection(float WidthOverHeight, float FOV)
{
float Near = 1.0f;
float Far = 100.0f;
float f = 1.0f/(float)tan(DegToRad(FOV / 2.0f));
float fn = 1.0f / (Near - Far);
float a = f / WidthOverHeight;
float b = f;
float c = Far * fn;
float d = Near * Far * fn;
m4 Result =
{
{{a, 0, 0, 0},
{0, b, 0, 0},
{0, 0, c, -1},
{0, 0, d, 0}}
};
return Result;
}
And here is the main code
m4 Project = Projection(ar, 90);
m4 Move = {};
CreateMat4(&Move,
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, -2,
0, 0, 0, 1);
m4 Rotate = Rotation(Scale);
Scale += 0.01f;
m4 FinalTransformation = Project * Move * Rotate;
SetShaderUniformMat4("Project", FinalTransformation, ShaderProgram);
Here are some pictures of the cube rotating.
In the shader code I just multiply the transformation by the position (with the transformation being on the left).
I am not sure if it's helpful but here is the rotation code:
float c = cos(Angle);
float s = sin(Angle);
m4 R =
{
{{ c, 0, s, 0},
{ 0, 1, 0, 0},
{-s, 0, c, 0},
{ 0, 0, 0, 1}}
};
return R;
I tried multiplying the matricies in the shader code instead of on the c++ side but then everything disappeared.
OpenGL matrixes are stored with column major order. You have to read the columns from left to right. For example the 1st column of the matrix R is { c, 0, s, 0}, the 2nd one is { 0, 1, 0, 0} the 3rd is {-s, 0, c, 0} and the 4th is { 0, 0, 0, 1}. The lines in your code are actually columns (not rows).
Therefore you need to to transpose you projection matrix (Project) and translation matrix (Move).
I performed an MVP transformation on the vertices of the model. In theory, I must apply the inverse transpose matrix of the MVP transformation to the normal.
This is the derivation process：
(A, B, C) is the normal of the plane where the point (x, y, z) lies
For a vector, such as (x0, y0, z0), it is (x0, y0, z0, 0) in homogeneous coordinates. After transformation, it should still be a vector, like (x1, y1, z1, 0), This requires that the last row of the 4 * 4 transformation matrix is all 0 except for the elements in the last column, otherwise it will become (x1, y1, z1, n) after the transformation.
In fact, my MVP transformation matrix cannot satisfy this point after undergoing inverse transpose transformation.
Code:
Mat<4, 4> View(const Vec3& pos){
Mat<4, 4> pan{1, 0, 0, -pos.x,
0, 1, 0, -pos.y,
0, 0, 1, -pos.z,
0, 0, 0, 1};
Vec3 v = Cross(camera.lookAt, camera.upDirection).Normalize();
Mat<4, 4> rotate{v.x, v.y, v.z, 0,
camera.upDirection.x, camera.upDirection.y, camera.upDirection.z, 0,
-camera.lookAt.x, -camera.lookAt.y, -camera.lookAt.z, 0,
0, 0, 0, 1};
return rotate * pan;
}
Mat<4, 4> Projection(double near, double far, double fov, double aspectRatio){
double angle = fov * PI / 180;
double t = -near * tan(angle / 2);
double b = -t;
double r = t * aspectRatio;
double l = -r;
Mat<4, 4> zoom{2 / (r - l), 0, 0, 0,
0, 2 / (t - b), 0, 0,
0, 0, 2 / (near - far), 0,
0, 0, 0, 1};
Mat<4, 4> pan{1, 0, 0, -(l + r) / 2,
0, 1, 0, -(t + b) / 2,
0, 0, 1, -(near + far) / 2,
0, 0, 0, 1};
Mat<4, 4> extrusion{near, 0, 0, 0,
0, near, 0, 0,
0, 0, near + far, -near * far,
0, 0, 1, 0};
Mat<4, 4> ret = zoom * pan * extrusion;
return ret;
}
Mat<4, 4> modelMatrix = Mat<4, 4>::identity();
Mat<4, 4> viewMatrix = View(camera.position);
Mat<4, 4> projectionMatrix = Projection(-0.1, -50, camera.fov, camera.aspectRatio);
Mat<4, 4> mvp = projectionMatrix * viewMatrix * modelMatrix;
Mat<4, 4> mvpInverseTranspose = mvp.Inverse().Transpose();
mvp:
-2.29032 0 0.763441 -2.68032e-16
0 -2.41421 0 0
-0.317495 0 -0.952486 2.97455
0.316228 0 0.948683 -3.16228
mvpInverseTranspose:
-0.392957 0 0.130986 0
0 -0.414214 0 0
-4.99 0 -14.97 -4.99
-4.69377 0 -14.0813 -5.01
I seem to understand the problem. The lighting should be calculated in world space, so I only need to apply the inverse transpose matrix of the model transformation to the normal.
How do you implement the rotation of the shape in place and the movement in a rotated state?
I want to move the rotated shape towards the x and y axes of the screen I see.
I have already made the shape move in the direction of the x-axis and y-axis when I press the key.
But I can't move the way I want to. It's weird.
How do I set up the code to move the way I want to?
I'll put the code up for now.
glTranslatef(2.5 + puzX1, 2 + puzY1, 0);
glRotatef(100, 0.0, 0.0, 1.0);
glRotatef(puzang1, 0.0, 0.0, 1.0);
glTranslatef(-2.5+puzX1, -2+puzY1, 0);
I wrote the code to make it spin in place.
The code at the top and bottom of the code is a code that moves to the center of the shape and then returns it to its place.
What should I add?
Which part should be modified?
I am not good at English.
i'm so sorry
Can you help me?
Note, that drawing by glBegin/glEnd sequences, the fixed function pipeline matrix stack, is deprecated since decades.
Read about Fixed Function Pipeline and see Vertex Specification and Shader for a state of the art way of rendering.
How do you implement the rotation of the shape in place?
If the shade should rotate on its local axis, then you have to do the rotation before the translation. In the code this means the rotation instruction has to be after the translation instruction:
glTranslatef(2.5 + puzX1, 2 + puzY1, 0);
glRotatef(puzang1, 0.0, 0.0, 1.0);
glRotatef(100, 0.0, 0.0, 1.0);
See also OpenGL translation before and after a rotation
Explanation:
Translation: See the documentation of glTranslate:
glTranslate produces a translation by x y z . The current matrix (see glMatrixMode) is multiplied by this translation matrix, with the product replacing the current matrix.
Rotation: See the documentation of glRotate:
glRotate produces a rotation of angle degrees around the vector x y z . The current matrix (see glMatrixMode) is multiplied by a rotation matrix with the product replacing the current matrix.
The translation matrix looks like this:
Matrix4x4 translate;
translate[0] : ( 1, 0, 0, 0 )
translate[1] : ( 0, 1, 0, 0 )
translate[2] : ( 0, 0, 1, 0 )
translate[3] : ( tx, ty, tz, 1 )
And the rotation matrix around Z-Axis looks like this:
Matrix4x4 rotate;
float angle;
rotate[0] : ( cos(angle), sin(angle), 0, 0 )
rotate[1] : ( -sin(angle), cos(angle), 0, 0 )
rotate[2] : ( 0, 0, 1, 0 )
rotate[3] : ( 0, 0, 0, 1 )
The result of translate * rotate is this:
glTranslate( ..... );
glRotate( ..... );
model[0] : ( cos(angle), sin(angle), 0, 0 )
model[1] : ( -sin(angle), cos(angle), 0, 0 )
model[2] : ( 0, 1, 0, 0 )
model[3] : ( tx, ty, tz, 1 )
The result of rotate * translate is:
glRotate( ..... );
glTranslate( ..... );
model[0] : ( cos(angle), sin(angle), 0, 0 )
model[1] : ( -sin(angle), cos(angle), 0, 0 )
model[2] : ( 0, 0, 1, 0 )
model[3] : ( cos(angle)*tx - sin(angle)*tx, sin(angle)*ty + cos(angle)*ty, tz, 1 )
I have a Hand mesh which I want to animate.
I have the Skeleton which can be hierarchically animated.
My mesh is also weighted in Blender. So each vertex has 4 associated bones to be affected by.
When I apply the Animation of my Skeleton to the mesh, the hierarchy is applied correctly. (so the hierarchy of the mesh, matches the hierarchy of the Skeleton).
So far so good, now question:
the fingers look to be stretched (its like the fingers smashed by a heavy door). Why?
Note: (I didnt apply the bind pose bone Transformation Matrix explicitly, but I read about it and I believe its functionality is there, in the hierarchical Transformation I have for my Skeleton).
If you need more clarification of the steps, please ask.
vector<glm::mat4> Posture1Hand::HierarchyApplied(HandSkltn HNDSKs){
vector <glm::mat4> Matrices;
Matrices.resize(HNDSKs.GetLimbNum());
//non Hierarchical Matrices
for (unsigned int i = 0; i < Matrices.size(); i++){
Matrices[i] = newPose[i].getModelMatSkltn(HNDSKs.GetLimb(i).getLwCenter());
}
for (unsigned int i = 0; i < Matrices.size(); i++){
vector<Limb*>childeren = HNDSKs.GetLimb(i).getChildren();
for (unsigned int j = 0; j < childeren.size(); j++){
Matrices[childeren[j]->getId()] = Matrices[i] * Matrices[childeren[j]->getId()];
}
}
return Matrices;
}
Here is my getModelMatSkltn method.
inline glm::mat4 getModelMatSkltn(const glm::vec3& RotationCentre) const{//to apply the rotation on the whole heirarchy
glm::mat4 posMatrix = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
posMatrix = glm::translate(posMatrix, newPos);
glm::mat4 trMatrix = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
glm::mat4 OriginTranslate = glm::translate(trMatrix, -RotationCentre);
glm::mat4 InverseTranslate = glm::translate(trMatrix, RotationCentre);
glm::mat4 rotXMatrix = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
rotXMatrix = glm::rotate(rotXMatrix, glm::radians(newRot.x), glm::vec3(1, 0, 0));
glm::mat4 rotYMatrix = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
rotYMatrix = glm::rotate(rotYMatrix, glm::radians(newRot.y), glm::vec3(0, 1, 0));
glm::mat4 rotZMatrix = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
rotZMatrix = glm::rotate(rotZMatrix, glm::radians(newRot.z), glm::vec3(0, 0, 1));
glm::mat4 scaleMatric = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
scaleMatric = glm::scale(scaleMatric, newScale);
glm::mat4 rotMatrix = rotZMatrix*rotYMatrix*rotXMatrix;
rotMatrix = InverseTranslate*rotMatrix*OriginTranslate;
return posMatrix*rotMatrix*scaleMatric;
}
and this is how I send 20 transformation Matrix (because of 20 joints in Hand) to GPU:
void GLShader::Update(const vector trMat, const GLCamera& camera){
vector<glm::mat4> MVP; MVP.resize(trMat.size());
for (unsigned int i = 0; i < trMat.size(); i++){
MVP[i] = camera.getViewProjection()* trMat[i];
}
glUniformMatrix4fv(newUniform[TRANSFORM_U], trMat.size(), GL_FALSE, &MVP[0][0][0]);//4 floating value
}
I guess one should be familiar with calculation of vertex position in the shader in order to be able to answer the question, but I send a part of my vertex shader too.
attribute vec3 position;
attribute vec2 texCoord;
attribute vec4 weight;
attribute vec4 weightInd;
uniform mat4 transform[20];//vector of uniform for 20 number of joints in my skleton
void main(){
mat4 WMat;//weighted matrix
float w;
int Index;
for (int i=0; i<4; i++){
Index=int(weightInd[i]);
w=weight[i];
WMat += w*transform[Index];
}
gl_Position= WMat*vec4(position, 1.0);
}
I have a camera, which is defined through an up vector, a position and a reference point (camera looks at this point). Furthermore I can calculate the view direction, of course.
Now I tried to reflect this camera in a plane (e.g. z = 0). My first attempt was to reflect every single vector in the plane with the belonging reflection matrix and looked like this:
mat4 mReflection = mat4(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, -1, 0,
0, 0, 0, 1);
up = mReflection * up;
position = mReflection * position;
lookAt = mReflection * lookAt;
But this didn't work very well and I don't know why. What is wrong with this method?