How do I manually apply an OpenGL translation matrix to a vertex? - opengl

Question

I have a specific need to apply a stored openGL matrix to a vertex by hand. I admit a weak spot with regards to matrix math, but I have read through all the documentation I can find and I'm reasonably sure I'm doing this correctly, but I'm getting an unexpected result. What am I missing?
(Note that this may be a math question, but I suspect I'm actually misunderstanding how to apply the translation matrix, so I thought I'd try here)
In the code snippet below, #1 works fine, #2 fails...
float x=1;
float y=1;
float z=1;
float w=1;
float x2=0;
float y2=0;
float z2=0;
float w2=1;
// 1 THIS WORKS:
glLoadIdentity();
// Convert from NSArray to C float
float modelMatrix[16];
for(int x=0;x<16;x++){modelMatrix[x]=[[cs.modelView objectAtIndex:x] floatValue];}
// Load the matrix the openGL way
glLoadMatrixf(modelMatrix);
// Custom function takes two coordinates and draws a box
[self drawBoxFromX:x FromY:y FromZ:z ToX:x2 ToY:y2 ToZ:z2];
//2 THIS DOES NOT WORK: Apply the matrix by hand
glLoadIdentity();
float new_x = (x*modelMatrix[0])+(y*modelMatrix[4])+(z*modelMatrix[8])+(w*modelMatrix[12]);
float new_y = (x*modelMatrix[1])+(y*modelMatrix[5])+(z*modelMatrix[9])+(w*modelMatrix[13]);
float new_z = (x*modelMatrix[2])+(y*modelMatrix[6])+(z*modelMatrix[10])+(w*modelMatrix[14]);
float new_x2 = (x2*modelMatrix[0])+(y2*modelMatrix[4])+(z2*modelMatrix[8])+(w2*modelMatrix[12]);
float new_y2 = (x2*modelMatrix[1])+(y2*modelMatrix[5])+(z2*modelMatrix[9])+(w2*modelMatrix[13]);
float new_z2 = (x2*modelMatrix[2])+(y2*modelMatrix[6])+(z2*modelMatrix[10])+(w2*modelMatrix[14]);
// Should draw a box identical to above, but gives strange result)
[self drawBoxFromX:new_x FromY:new_y FromZ:new_z ToX:new_x2 ToY:new_y2 ToZ:new_z2];
Update:
Based on a helpful comment below I realized I was only rotating two of the vertexes rather than all 8 of the cube. The following code works as expected, posting here for anyone who runs into a similar problem wrapping their head around 3d/opengl stuff. (Note: In case it is not obvious, this is not production code. There are many more efficient and less manual ways multiply matrices and describe cubes (see comments). The purpose of this code is simply to explicitly illustrate a behavior.)
struct Cube myCube;
myCube.a1.x=-1;
myCube.a1.y=-1;
myCube.a1.z=-1;
myCube.b1.x=-1;
myCube.b1.y=-1;
myCube.b1.z=1;
myCube.c1.x=1;
myCube.c1.y=-1;
myCube.c1.z=1;
myCube.d1.x=1;
myCube.d1.y=-1;
myCube.d1.z=-1;
myCube.a2.x=-1;
myCube.a2.y=1;
myCube.a2.z=-1;
myCube.b2.x=-1;
myCube.b2.y=1;
myCube.b2.z=1;
myCube.c2.x=1;
myCube.c2.y=1;
myCube.c2.z=1;
myCube.d2.x=1;
myCube.d2.y=1;
myCube.d2.z=-1;
//1 Load modelview and draw a box (this works fine)
glLoadIdentity();
float modelMatrix[16];
for(int x=0;x<16;x++){modelMatrix[x]=[[cs.modelView objectAtIndex:x] floatValue];}
glLoadMatrixf(modelMatrix);
[self drawCube:myCube];
//2 Load the matrix by hand (identical to above)
glLoadIdentity();
float w=1;
float new_Ax = (myCube.a1.x*modelMatrix[0])+(myCube.a1.y*modelMatrix[4])+(myCube.a1.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_Ay = (myCube.a1.x*modelMatrix[1])+(myCube.a1.y*modelMatrix[5])+(myCube.a1.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_Az = (myCube.a1.x*modelMatrix[2])+(myCube.a1.y*modelMatrix[6])+(myCube.a1.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_Bx = (myCube.b1.x*modelMatrix[0])+(myCube.b1.y*modelMatrix[4])+(myCube.b1.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_By = (myCube.b1.x*modelMatrix[1])+(myCube.b1.y*modelMatrix[5])+(myCube.b1.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_Bz = (myCube.b1.x*modelMatrix[2])+(myCube.b1.y*modelMatrix[6])+(myCube.b1.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_Cx = (myCube.c1.x*modelMatrix[0])+(myCube.c1.y*modelMatrix[4])+(myCube.c1.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_Cy = (myCube.c1.x*modelMatrix[1])+(myCube.c1.y*modelMatrix[5])+(myCube.c1.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_Cz = (myCube.c1.x*modelMatrix[2])+(myCube.c1.y*modelMatrix[6])+(myCube.c1.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_Dx = (myCube.d1.x*modelMatrix[0])+(myCube.d1.y*modelMatrix[4])+(myCube.d1.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_Dy = (myCube.d1.x*modelMatrix[1])+(myCube.d1.y*modelMatrix[5])+(myCube.d1.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_Dz = (myCube.d1.x*modelMatrix[2])+(myCube.d1.y*modelMatrix[6])+(myCube.d1.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_A2x = (myCube.a2.x*modelMatrix[0])+(myCube.a2.y*modelMatrix[4])+(myCube.a2.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_A2y = (myCube.a2.x*modelMatrix[1])+(myCube.a2.y*modelMatrix[5])+(myCube.a2.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_A2z = (myCube.a2.x*modelMatrix[2])+(myCube.a2.y*modelMatrix[6])+(myCube.a2.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_B2x = (myCube.b2.x*modelMatrix[0])+(myCube.b2.y*modelMatrix[4])+(myCube.b2.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_B2y = (myCube.b2.x*modelMatrix[1])+(myCube.b2.y*modelMatrix[5])+(myCube.b2.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_B2z = (myCube.b2.x*modelMatrix[2])+(myCube.b2.y*modelMatrix[6])+(myCube.b2.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_C2x = (myCube.c2.x*modelMatrix[0])+(myCube.c2.y*modelMatrix[4])+(myCube.c2.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_C2y = (myCube.c2.x*modelMatrix[1])+(myCube.c2.y*modelMatrix[5])+(myCube.c2.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_C2z = (myCube.c2.x*modelMatrix[2])+(myCube.c2.y*modelMatrix[6])+(myCube.c2.z*modelMatrix[10])+(w*modelMatrix[14]);
float new_D2x = (myCube.d2.x*modelMatrix[0])+(myCube.d2.y*modelMatrix[4])+(myCube.d2.z*modelMatrix[8])+(w*modelMatrix[12]);
float new_D2y = (myCube.d2.x*modelMatrix[1])+(myCube.d2.y*modelMatrix[5])+(myCube.d2.z*modelMatrix[9])+(w*modelMatrix[13]);
float new_D2z = (myCube.d2.x*modelMatrix[2])+(myCube.d2.y*modelMatrix[6])+(myCube.d2.z*modelMatrix[10])+(w*modelMatrix[14]);
myCube.a1.x=new_Ax;
myCube.a1.y=new_Ay;
myCube.a1.z=new_Az;
myCube.b1.x=new_Bx;
myCube.b1.y=new_By;
myCube.b1.z=new_Bz;
myCube.c1.x=new_Cx;
myCube.c1.y=new_Cy;
myCube.c1.z=new_Cz;
myCube.d1.x=new_Dx;
myCube.d1.y=new_Dy;
myCube.d1.z=new_Dz;
myCube.a2.x=new_A2x;
myCube.a2.y=new_A2y;
myCube.a2.z=new_A2z;
myCube.b2.x=new_B2x;
myCube.b2.y=new_B2y;
myCube.b2.z=new_B2z;
myCube.c2.x=new_C2x;
myCube.c2.y=new_C2y;
myCube.c2.z=new_C2z;
myCube.d2.x=new_D2x;
myCube.d2.y=new_D2y;
myCube.d2.z=new_D2z;
[self drawCube:myCube];

Answer 1

Drawing a rotated box is not the same as rotating two of the box corners and then drawing an axis-parallel box. The simplest way to draw a transformed 3D box is to transform all 8 vertices.