I'm having some trouble with drawing a circle with direct2D. I have a potentiometer device that I rotate in a circle, and as I do the value of Ch1_Data_ThreadShared (which is a float variable) changes. 0 degrees and 360 degrees correspond to a value of .5 and 4.5 in the Ch1_Data_ThreadShared variable. I convert those values to radians and then since I was having issues I constrained it so the value would always be between 0 and 2pi. Then I create my x and y coordinates so the ellipse object moves in a circle on the screen.
// Create x and y coordinates to rotate in a circle as Ch1_Data_ThreadShared value changes
float Ch1_Data_ThreadSharedConvertedToRadians = (Ch0_Data_ThreadShared-.5) * .5 * pi;
if (Ch1_Data_ThreadSharedConvertedToRadians > (2 * pi))
Ch1_Data_ThreadSharedConvertedToRadians = (2 * pi);
if (Ch1_Data_ThreadSharedConvertedToRadians < 0)
Ch1_Data_ThreadSharedConvertedToRadians = 0;
float Ch1_Data_ThreadSharedConvertedToRadiansXValue = 200 * (cos(Ch1_Data_ThreadSharedConvertedToRadians));
float Ch1_Data_ThreadSharedConvertedToRadiansYValue = 200 * (sin(Ch1_Data_ThreadSharedConvertedToRadians));
And then this is where I later in the code draw the circle. When I run it the ellipse object moves in a perfect smooth circle on the screen as expected, except for when it shifts from 0 radians to 2pi radians (or the other way around). At that point, the ellipse object shifts randomly to another part of the screen for a brief moment and then continues along it's expected path.
Is this a weird quirk with drawing in direct2D? Or is there something in my math that's missing?
// Draw Ellipse
graphics->DrawEllipse(400.0f + Ch1_Data_ThreadShared*100, 400.0f, // position
50.0f, 50.0f, // radius
1.0f, 0.2f, 0.2f, 0.2f, // fill color
1.0f, 0.9f, 0.9f, 0.9f, // line color
0.0f, // line width
45.0f, // object rotation (degrees)
1.0f, 1.0f); // object scaling in the x and y directions
graphics->SetTransformToIdentity(); // if apply transformation then need to reset this otherwise it will carry to next object
My question is simple, how do I draw a cylinder in modern OpenGL? I'm using GLFW together with OpenGL 3.x. My thought at first was to create a function that computes the vertex positions at the bottom and at the top as circles and then draw lines between these vertices. But I have no idea how to implement this.. Does anyone have a good solution?
You can do that with a triangle strip and generate a vertex at the bottom then one at the top. That should generate the sides easily. Then just generate the caps with a triangle fan and you are don. To simplify things you can use the modelview matrix to move the cylinder into position where you want. This way you only need to have a circle in the x/y plane or similar so the math is very simple.
For performance consider using precompiled objects and/or vertex arrays.
I have been using this for a while now and I hope it will help people in the future.
struct {
GLfloat x,z, y_start, y_end;
}each_pole; // struct
std::vector<each_pole> each_pole_vector; // vector of structs
//Cylinder with y axis up
GLfloat cylinder_height = 1.0f,
cylinder_radius = 0.5f,
nr_of_points_cylinder = 360.f;
for (int i = 0; i < nr_of_points_cylinder; ++i)
{
GLfloat u = i / (GLfloat)nr_of_points_cylinder;
//Where the cylinder is in the x and z positions (3D space)
each_pole.x = center.x
+ cylinder_radius*cos(2*M_PI*u);
each_pole.z = center.z
+ cylinder_radius*sin(2*M_PI*u);
each_pole.y_start = 0.0f;
each_pole.y_end = cylinder_height;
each_pole_vector.push_back(each_pole);
}
return each_pole_vector;
So I want to use quaternions and angles to control my camera using my mouse.
I accumulate the vertical/horizontal angles like this:
void Camera::RotateCamera(const float offsetHorizontalAngle, const float offsetVerticalAngle)
{
mHorizontalAngle += offsetHorizontalAngle;
mHorizontalAngle = std::fmod(mHorizontalAngle, 360.0f);
mVerticalAngle += offsetVerticalAngle;
mVerticalAngle = std::fmod(mVerticalAngle, 360.0f);
}
and compute my orientation like this:
Mat4 Camera::Orientation() const
{
Quaternion rotation;
rotation = glm::angleAxis(mVerticalAngle, Vec3(1.0f, 0.0f, 0.0f));
rotation = rotation * glm::angleAxis(mHorizontalAngle, Vec3(0.0f, 1.0f, 0.0f));
return glm::toMat4(rotation);
}
and the forward vector, which I need for glm::lookAt, like this:
Vec3 Camera::Forward() const
{
return Vec3(glm::inverse(Orientation()) * Vec4(0.0f, 0.0f, -1.0f, 0.0f));
}
I think that should do the trick, but I do not know how in my example game to get actual angles? All I have is the current and previous mouse location in window coordinates.. how can I get proper angles from that?
EDIT: on a second thought.. my "RotateCamera()" cant be right; I am experiencing rubber-banding effect due to the angles reseting after reaching 360 deegres... so how do I accumulate angles properly? I can just sum them up endlessly
Take a cross section of the viewing frustum (the blue circle is your mouse position):
Theta is half of your FOV
p is your projection plane distance (don't worry - it will cancel out)
From simple ratios it is clear that:
But from simple trignometry
So ...
Just calculate the angle psi for each of your mouse positions and subtract to get the difference.
A similar formula can be found for the vertical angle:
Where A is your aspect ratio (width / height)
When I first load my object I calculate the initial AABB with the maximum and minimum (x,y,z) points. But this is in object space and the object moves around the world and more importantly, rotates.
How do I recalculate the new AABB every time the object is translated/rotated? This happens basically in every frame. Is it going to be a very intensive operation to recalculate the new AABB every frame? If so, what would be the alternative?
I know AABBs will make my collision detection less accurate, but it's easier to implement the collision detection code than OBBs and I want to take this one step at a time.
Here's my current code after some insight from the answers below:
typedef struct sAxisAlignedBoundingBox {
Vector3D bounds[8];
Vector3D max, min;
} AxisAlignedBoundingBox;
void drawAxisAlignedBoundingBox(AxisAlignedBoundingBox box) {
glPushAttrib(GL_LIGHTING_BIT | GL_POLYGON_BIT);
glEnable(GL_COLOR_MATERIAL);
glDisable(GL_LIGHTING);
glColor3f(1.0f, 1.0f, 0.0f);
glBegin(GL_LINE_LOOP);
glVertex3f(box.bounds[0].x, box.bounds[0].y, box.bounds[0].z);
glVertex3f(box.bounds[1].x, box.bounds[1].y, box.bounds[1].z);
glVertex3f(box.bounds[2].x, box.bounds[2].y, box.bounds[2].z);
glVertex3f(box.bounds[3].x, box.bounds[3].y, box.bounds[3].z);
glEnd();
glBegin(GL_LINE_LOOP);
glVertex3f(box.bounds[4].x, box.bounds[4].y, box.bounds[4].z);
glVertex3f(box.bounds[5].x, box.bounds[5].y, box.bounds[5].z);
glVertex3f(box.bounds[6].x, box.bounds[6].y, box.bounds[6].z);
glVertex3f(box.bounds[7].x, box.bounds[7].y, box.bounds[7].z);
glEnd();
glBegin(GL_LINE_LOOP);
glVertex3f(box.bounds[0].x, box.bounds[0].y, box.bounds[0].z);
glVertex3f(box.bounds[5].x, box.bounds[5].y, box.bounds[5].z);
glVertex3f(box.bounds[6].x, box.bounds[6].y, box.bounds[6].z);
glVertex3f(box.bounds[1].x, box.bounds[1].y, box.bounds[1].z);
glEnd();
glBegin(GL_LINE_LOOP);
glVertex3f(box.bounds[4].x, box.bounds[4].y, box.bounds[4].z);
glVertex3f(box.bounds[7].x, box.bounds[7].y, box.bounds[7].z);
glVertex3f(box.bounds[2].x, box.bounds[2].y, box.bounds[2].z);
glVertex3f(box.bounds[3].x, box.bounds[3].y, box.bounds[3].z);
glEnd();
glPopAttrib();
}
void calculateAxisAlignedBoundingBox(GLMmodel *model, float matrix[16]) {
AxisAlignedBoundingBox box;
float dimensions[3];
// This will give me the absolute dimensions of the object
glmDimensions(model, dimensions);
// This calculates the max and min points in object space
box.max.x = dimensions[0] / 2.0f, box.min.x = -1.0f * box.max.x;
box.max.y = dimensions[1] / 2.0f, box.min.y = -1.0f * box.max.y;
box.max.z = dimensions[2] / 2.0f, box.min.z = -1.0f * box.max.z;
// These calculations are probably the culprit but I don't know what I'm doing wrong
box.max.x = matrix[0] * box.max.x + matrix[4] * box.max.y + matrix[8] * box.max.z + matrix[12];
box.max.y = matrix[1] * box.max.x + matrix[5] * box.max.y + matrix[9] * box.max.z + matrix[13];
box.max.z = matrix[2] * box.max.x + matrix[6] * box.max.y + matrix[10] * box.max.z + matrix[14];
box.min.x = matrix[0] * box.min.x + matrix[4] * box.min.y + matrix[8] * box.min.z + matrix[12];
box.min.y = matrix[1] * box.min.x + matrix[5] * box.min.y + matrix[9] * box.min.z + matrix[13];
box.min.z = matrix[2] * box.min.x + matrix[6] * box.min.y + matrix[10] * box.min.z + matrix[14];
/* NOTE: If I remove the above calculations and do something like this:
box.max = box.max + objPlayer.position;
box.min = box.min + objPlayer.position;
The bounding box will move correctly when I move the player, the same does not
happen with the calculations above. It makes sense and it's very simple to move
the box like this. The only problem is when I rotate the player, the box should
be adapted and increased/decreased in size to properly fit the object as a AABB.
*/
box.bounds[0] = Vector3D(box.max.x, box.max.y, box.min.z);
box.bounds[1] = Vector3D(box.min.x, box.max.y, box.min.z);
box.bounds[2] = Vector3D(box.min.x, box.min.y, box.min.z);
box.bounds[3] = Vector3D(box.max.x, box.min.y, box.min.z);
box.bounds[4] = Vector3D(box.max.x, box.min.y, box.max.z);
box.bounds[5] = Vector3D(box.max.x, box.max.y, box.max.z);
box.bounds[6] = Vector3D(box.min.x, box.max.y, box.max.z);
box.bounds[7] = Vector3D(box.min.x, box.min.y, box.max.z);
// This draw call is for testing porpuses only
drawAxisAlignedBoundingBox(box);
}
void drawObjectPlayer(void) {
static float mvMatrix[16];
if(SceneCamera.GetActiveCameraMode() == CAMERA_MODE_THIRD_PERSON) {
objPlayer.position = SceneCamera.GetPlayerPosition();
objPlayer.rotation = SceneCamera.GetRotationAngles();
objPlayer.position.y += -PLAYER_EYE_HEIGHT + 0.875f;
/* Only one of the two code blocks below should be active at the same time
Neither of them is working as expected. The bounding box doesn't is all
messed up with either code. */
// Attempt #1
glPushMatrix();
glTranslatef(objPlayer.position.x, objPlayer.position.y, objPlayer.position.z);
glRotatef(objPlayer.rotation.y + 180.0f, 0.0f, 1.0f, 0.0f);
glCallList(gameDisplayLists.player);
glGetFloatv(GL_MODELVIEW_MATRIX, mvMatrix);
glPopMatrix();
// Attempt #2
glPushMatrix();
glLoadIdentity();
glTranslatef(objPlayer.position.x, objPlayer.position.y, objPlayer.position.z);
glRotatef(objPlayer.rotation.y + 180.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, mvMatrix);
glPopMatrix();
calculateAxisAlignedBoundingBox(objPlayer.model, mvMatrix);
}
}
But it doesn't work as it should... What I'm doing wrong?
Simply recompute the AABB of the transformed AABB. This means transforming 8 vertices (8 vertex - matrix multiplications) and 8 vertex-vertex comparisons.
So at initialisation, you compute your AABB in model space: for each x,y,z of each vertex of the model, you check against xmin, xmax, ymin, ymax, etc.
For each frame, you generate a new transformation matrix. In OpenGL this is done with glLoadIdentity followed by glTransform/Rotate/Scale (if using the old API). This is the Model Matrix, as lmmilewski said.
You compute this transformation matrix a second time (outside OpenGL, for instance using glm). You also can get OpenGL's resulting matrix using glGet.
You multiply each of your AABB's eight vertices by this matrix. Use glm for matrix-vector multiplication. You'll get your transformed AABB (in world space). It it most probably rotated (not axis-aligned anymore).
Now your algorithm probably only work with axis-aligned stuff, hence your question. So now you approximate the new bounding box of the transformed model by takinf the bounding box of the transformed bounding box:
For each x,y,z of each vertex of the new AABB, you check against xmin, xmax, ymin, ymax, etc. This gives you an world-space AABB that you can use in your clipping algorithm.
This is not optimal (AABB-wise). You'll get lots of empty space, but performance-wise, it's much much better that recomputing the AABB of the whole mesh.
As for the transformation matrix, in drawObjectPlayer:
gLLoadIdentity();
glTranslatef(objPlayer.position.x, objPlayer.position.y, objPlayer.position.z);
glRotatef(objPlayer.rotation.y + 180.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, mvMatrix);
// Now you've got your OWN Model Matrix (don't trust the GL_MODELVIEW_MATRIX flag : this is a workaround, and I know what I'm doing ^^ )
gLLoadIdentity(); // Reset the matrix so that you won't make the transformations twice
gluLookAt( whatever you wrote here earlier )
glTranslatef(objPlayer.position.x, objPlayer.position.y, objPlayer.position.z);
glRotatef(objPlayer.rotation.y + 180.0f, 0.0f, 1.0f, 0.0f);
// Now OpenGL is happy, he's got his MODELVIEW matrix correct ( gluLookAt is the VIEW part; Translate/Rotate is the MODEL part
glCallList(gameDisplayLists.player); // Transformed correcty
I can't explain it further than that... as said in the comments, you had to do it twice. You wouldn't have these problems and ugly workarounds in OpenGL 3, btw, because you'd be fully responsible of your own matrices. Equivalent in OpenGL 2:
glm::mat4 ViewMatrix = glm::LookAt(...);
glm::mat4 ModelMatrix = glm::rotate() * glm::translate(...);
// Use ModelMatrix for whatever you want
glm::mat4 ModelViewMatrix = ViewMatrix * ModelMatrix;
glLoadMatrix4fv( &ModelViewMatrix[0][0] ); // In OpenGL 3 you would use an uniform instead
Much cleaner, right?
Yep, you can transform the eight corner vertices and do min/max on the results, but there is a faster way, as described by Jim Arvo from his chapter in Graphics Gems (1990).
Performance-wise, Arvo's method is roughly equivalent to two transforms instead of eight and basically goes as follows (this transforms box A into box B)
// Split the transform into a translation vector (T) and a 3x3 rotation (M).
B = zero-volume AABB at T
for each element (i,j) of M:
a = M[i][j] * A.min[j]
b = M[i][j] * A.max[j]
B.min[i] += a < b ? a : b
B.max[i] += a < b ? b : a
return B
One variation of Arvo's method uses center / extent representation rather than mix / max, which is described by Christer Ericson in Real-Time Collision Detection (photo).
Complete C code for Graphics Gems article can be found here.
To do that you have to loop over every vertex, calculate its position in the world (multiply by modelview) and find the minimum / maximum vertex coordinates within every object (just like when you compute it for the first time).
You can scale your AABB a bit, so that you don't have to recalculate it - it is enough to enlarge it by factor sqrt(2) - your rotated object then always fits in AABB.
There is also a question in which direction you rotate(?). If always in one then you can enlarge AABB only in that direction.
Optionally, you can use bounding spheres instead of AABBs. Then you don't care about rotation and scaling is not a problem.
To quote a previous response on AABB # Stack Overflow:
"Sadly yes, if your character rotates you need to recalculate your AABB . . .
Skurmedel
The respondent's suggestion, and mine, is to implement oriented bounding boxes once you have AABB working, and also to note you can make aabb's of portions of a mesh to fudge collision detection with greater accuracy than one enormous box for each object.
Why not use your GPU? Today I implimented a solution of this problem by rendening a couple of frames.
Temporary place your camera over the object, above it, pointing
down at the object.
Render only your object, with out lights or
anything.
Use orthographic projection too.
Then read the frame buffer. Rows and columns of black pixels means the model isn't there. Hit a white pixel - you hit one of the model AABB borders.
I know this isn't a solution for all the cases, but with some prior knowledge, this is very efficient.
For rendering off screen see here.
I want to know how to draw a spiral.
I wrote this code:
void RenderScene(void)
{
glClear(GL_COLOR_BUFFER_BIT);
GLfloat x,y,z = -50,angle;
glBegin(GL_POINTS);
for(angle = 0; angle < 360; angle += 1)
{
x = 50 * cos(angle);
y = 50 * sin(angle);
glVertex3f(x,y,z);
z+=1;
}
glEnd();
glutSwapBuffers();
}
If I don't include the z terms I get a perfect circle but when I include z, then I get 3 dots that's it. What might have happened?
I set the viewport using glviewport(0,0,w,h)
To include z should i do anything to set viewport in z direction?
You see points because you are drawing points with glBegin(GL_POINTS).
Try replacing it by glBegin(GL_LINE_STRIP).
NOTE: when you saw the circle you also drew only points, but drawn close enough to appear as a connected circle.
Also, you may have not setup the depth buffer to accept values in the range z = [-50, 310] that you use. These arguments should be provided as zNear and zFar clipping planes in your gluPerspective, glOrtho() or glFrustum() call.
NOTE: this would explain why with z value you only see a few points: the other points are clipped because they are outside the z-buffer range.
UPDATE AFTER YOU HAVE SHOWN YOUR CODE:
glOrtho(-100*aspectratio,100*aspectratio,-100,100,1,-1); would only allow z-values in the [-1, 1] range, which is why only the three points with z = -1, z = 0 and z = 1 will be drawn (thus 3 points).
Finally, you're probably viewing the spiral from the top, looking directly in the direction of the rotation axis. If you are not using a perspective projection (but an isometric one), the spiral will still show up as a circle. You might want to change your view with gluLookAt().
EXAMPLE OF SETTING UP PERSPECTIVE
The following code is taken from the excellent OpenGL tutorials by NeHe:
glViewport(0, 0, width, height);
glMatrixMode(GL_PROJECTION); // Select The Projection Matrix
glLoadIdentity(); // Reset The Projection Matrix
// Calculate The Aspect Ratio Of The Window
gluPerspective(45.0f,(GLfloat)width/(GLfloat)height,0.1f,100.0f);
glMatrixMode(GL_MODELVIEW); // Select The Modelview Matrix
glLoadIdentity(); // Reset The Modelview Matrix
Then, in your draw loop would look something like this:
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // Clear The Screen And The Depth Buffer
glLoadIdentity();
glTranslatef(-1.5f,0.0f,-6.0f); // Move Left 1.5 Units And Into The Screen 6.0
glBegin(GL_TRIANGLES); // Drawing Using Triangles
glVertex3f( 0.0f, 1.0f, 0.0f); // Top
glVertex3f(-1.0f,-1.0f, 0.0f); // Bottom Left
glVertex3f( 1.0f,-1.0f, 0.0f); // Bottom Right
glEnd();
Of course, you should alter this example code your needs.
catchmeifyoutry provides a perfectly capable method, but will not draw a spatially accurate 3D spiral, as any render call using a GL_LINE primitive type will rasterize to fixed pixel width. This means that as you change your perspective / view, the lines will not change width. In order to accomplish this, use a geometry shader in combination with GL_LINE_STRIP_ADJACENCY to create 3D geometry that can be rasterized like any other 3D geometry. (This does require that you use the post fixed-function pipeline however)
I recommended you to try catchmeifyoutry's method first as it will be much simpler. If you are not satisfied, try the method I described. You can use the following post as guidance:
http://prideout.net/blog/?tag=opengl-tron
Here is my Spiral function in C. The points are saved into a list which can be easily drawn by OpenGL (e.g. connect adjacent points in list with GL_LINES).
cx,cy ... spiral centre x and y coordinates
r ... max spiral radius
num_segments ... number of segments the spiral will have
SOME_LIST* UniformSpiralPoints(float cx, float cy, float r, int num_segments)
{
SOME_LIST *sl = newSomeList();
int i;
for(i = 0; i < num_segments; i++)
{
float theta = 2.0f * 3.1415926f * i / num_segments; //the current angle
float x = (r/num_segments)*i * cosf(theta); //the x component
float y = (r/num_segments)*i * sinf(theta); //the y component
//add (x + cx, y + cy) to list sl
}
return sl;
}
An example image with r = 1, num_segments = 1024:
P.S. There is difference in using cos(double) and cosf(float).
You use a float variable for a double function cos.