I’ve got a little objective-c utility program that renders a convex hull. (This is to troubleshoot a bug in another program that calculates the convex hull in preparation for spatial statistical analysis). I’m trying to render a set of triangles, each with an outward-pointing vector. I can get the triangles without problems, but the vectors are driving me crazy.
I’d like the vectors to be simple cylinders. The problem is that I can’t just declare coordinates for where the top and bottom of the cylinders belong in 3D (e.g., like I can for the triangles). I have to make them and then rotate and translate them from their default position along the z-axis. I’ve read a ton about Euler angles, and angle-axis rotations, and quaternions, most of which is relevant, but not directed at what I need: most people have a set of objects and then need to rotate the object in response to some input. I need to place the object correctly in the 3D “scene”.
I’m using the Cocoa3DTutorial classes to help me out, and they work great as far as I can tell, but the rotation bit is killing me.
Here is my current effort. It gives me cylinders that are located correctly, but all point along the z-axis (as in this image:
. We are looking in the -z direction. The triangle poking out behind is not part of the hull; for testing/debugging. The orthogonal cylinders are coordinate axes, more or less, and the spheres are to make sure the axes are located correctly, since I have to use rotation to place those cylinders correctly. And BTW, when I use that algorithm, the out-vectors fail as well, although in a different way, coming out normal to the planes, but all pointing in +z instead of some in -z)
from Render3DDocument.m:
// Make the out-pointing vector
C3DTCylinder *outVectTube;
C3DTEntity *outVectEntity;
Point3DFloat *sideCtr = [thisSide centerOfMass];
outVectTube = [C3DTCylinder cylinderWithBase: tubeRadius top: tubeRadius height: tubeRadius*10 slices: 16 stacks: 16];
outVectEntity = [C3DTEntity entityWithStyle:triColor
geometry:outVectTube];
Point3DFloat *outVect = [[thisSide inVect] opposite];
Point3DFloat *unitZ = [Point3DFloat pointWithX:0 Y:0 Z:1.0f];
Point3DFloat *rotAxis = [outVect crossWith:unitZ];
double rotAngle = [outVect angleWith:unitZ];
[outVectEntity setRotationX: rotAxis.x
Y: rotAxis.y
Z: rotAxis.z
W: rotAngle];
[outVectEntity setTranslationX:sideCtr.x - ctrX
Y:sideCtr.y - ctrY
Z:sideCtr.z - ctrZ];
[aScene addChild:outVectEntity];
(Note that Point3DFloat is basically a vector class, and that a Side (like thisSide) is a set of four Point3DFloats, one for each vertex, and one for a vector that points towards the center of the hull).
from C3DTEntity.m:
if (_hasTransform) {
glPushMatrix();
// Translation
if ((_translation.x != 0.0) || (_translation.y != 0.0) || (_translation.z != 0.0)) {
glTranslatef(_translation.x, _translation.y, _translation.z);
}
// Scaling
if ((_scaling.x != 1.0) || (_scaling.y != 1.0) || (_scaling.z != 1.0)) {
glScalef(_scaling.x, _scaling.y, _scaling.z);
}
// Rotation
glTranslatef(-_rotationCenter.x, -_rotationCenter.y, -_rotationCenter.z);
if (_rotation.w != 0.0) {
glRotatef(_rotation.w, _rotation.x, _rotation.y, _rotation.z);
} else {
if (_rotation.x != 0.0)
glRotatef(_rotation.x, 1.0f, 0.0f, 0.0f);
if (_rotation.y != 0.0)
glRotatef(_rotation.y, 0.0f, 1.0f, 0.0f);
if (_rotation.z != 0.0)
glRotatef(_rotation.z, 0.0f, 0.0f, 1.0f);
}
glTranslatef(_rotationCenter.x, _rotationCenter.y, _rotationCenter.z);
}
I added the bit in the above code that uses a single rotation around an axis (the “if (_rotation.w != 0.0)” bit), rather than a set of three rotations. My code is likely the problem, but I can’t see how.
The problem appears to be in that glrotatef() expects degrees and I was giving it radians. In addition, clockwise rotation is taken to be positive, and so the sign of the rotation was wrong. This is the corrected code:
I can now see that my other program has the inVects wrong (the outVects below are poking through the hull instead of pointing out from each face), and I can now track down that bug in the other program…tomorrow:
