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Question

我特别需要手动将存储的openGL矩阵应用于顶点。我承认在矩阵数学方面存在一个弱点，但我已经阅读了我能找到的所有文档，我有理由相信我正确地做到了这一点，但是我得到了意想不到的结果。我错过了什么？

（请注意，这可能是一个数学问题，但我怀疑我实际上误解了如何应用翻译矩阵，所以我想我会在这里尝试）

在下面的代码段中，＃1工作正常，＃2失败......

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];

更新

基于下面的有用评论，我意识到我只旋转了两个顶点，而不是旋转了所有8个立方体。下面的代码按预期工作，发布在这里为任何遇到类似问题的人围绕3d / opengl的东西。（注意：如果不明显，这不是生产代码。有许多更有效和更少手动的方法乘法矩阵和描述多维数据集（请参阅注释）。此代码的目的仅仅是明确说明行为。）< / p>

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

绘制旋转的框与旋转其中两个框角并绘制轴平行框不同。绘制变换后的3D框的最简单方法是变换所有8个顶点。

如何手动将OpenGL转换矩阵应用于顶点？

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1 个答案: