iOS：据我所知，GLKit 矩阵乘法已损坏
这是源代码。 ANSWER 是正确答案，RESULT 是实际结果。
我是盲目的，还是它为条目 33 计算了 -1，而它应该是 1？
这是代码：
GLKMatrix4 a = GLKMatrix4Make(-1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, 0.000000,
0.000000, 0.000000, -1.000000, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000);
GLKMatrix4 b = GLKMatrix4Make(1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, -1.000000,
0.000000, 0.000000, 1.000000, -1.000000,
0.000000, 0.000000, 0.000000, 1.000000);
GLKMatrix4 ANSWER = GLKMatrix4Make(-1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, -1.000000,
0.000000, 0.000000, -1.000000, 1.000000,
0.000000, 0.000000, 0.000000, 1.000000);
NSLog(@"##################################################");
GLKMatrix4 RESULT = GLKMatrix4Multiply(a,b);
NSLog(@"Result:");
NSLog(@" %f %f %f %f",RESULT.m00,RESULT.m01,RESULT.m02,RESULT.m03);
NSLog(@" %f %f %f %f",RESULT.m10,RESULT.m11,RESULT.m12,RESULT.m13);
NSLog(@" %f %f %f %f",RESULT.m20,RESULT.m21,RESULT.m22,RESULT.m23);
NSLog(@" %f %f %f %f",RESULT.m30,RESULT.m31,RESULT.m32,RESULT.m33);
NSLog(@"Answer:");
NSLog(@" %f %f %f %f",ANSWER.m00,ANSWER.m01,ANSWER.m02,ANSWER.m03);
NSLog(@" %f %f %f %f",ANSWER.m10,ANSWER.m11,ANSWER.m12,ANSWER.m13);
NSLog(@" %f %f %f %f",ANSWER.m20,ANSWER.m21,ANSWER.m22,ANSWER.m23);
NSLog(@" %f %f %f %f",ANSWER.m30,ANSWER.m31,ANSWER.m32,ANSWER.m33);
NSLog(@"##################################################");
这是输出：
##################################################
Result:
-1.000000 0.000000 0.000000 0.000000
0.000000 1.000000 0.000000 -1.000000
0.000000 0.000000 -1.000000 -1.000000
0.000000 0.000000 0.000000 1.000000
Answer:
-1.000000 0.000000 0.000000 0.000000
0.000000 1.000000 0.000000 -1.000000
0.000000 0.000000 -1.000000 1.000000
0.000000 0.000000 0.000000 1.000000
##################################################
我花了过去 5 个小时尝试调试一些 OpenGL 代码，结果发现这就是问题所在。我肯定错过了一些东西。任何人都可以发现发生了什么，或者验证这不应该发生吗？
Here's the source code. ANSWER is the correct answer, RESULT is the actual result.
Am I blind, or is it calculating a -1 for entry 33 when it should be a 1?
Here's the code:
GLKMatrix4 a = GLKMatrix4Make(-1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, 0.000000,
0.000000, 0.000000, -1.000000, 0.000000,
0.000000, 0.000000, 0.000000, 1.000000);
GLKMatrix4 b = GLKMatrix4Make(1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, -1.000000,
0.000000, 0.000000, 1.000000, -1.000000,
0.000000, 0.000000, 0.000000, 1.000000);
GLKMatrix4 ANSWER = GLKMatrix4Make(-1.000000, 0.000000, 0.000000, 0.000000,
0.000000, 1.000000, 0.000000, -1.000000,
0.000000, 0.000000, -1.000000, 1.000000,
0.000000, 0.000000, 0.000000, 1.000000);
NSLog(@"##################################################");
GLKMatrix4 RESULT = GLKMatrix4Multiply(a,b);
NSLog(@"Result:");
NSLog(@" %f %f %f %f",RESULT.m00,RESULT.m01,RESULT.m02,RESULT.m03);
NSLog(@" %f %f %f %f",RESULT.m10,RESULT.m11,RESULT.m12,RESULT.m13);
NSLog(@" %f %f %f %f",RESULT.m20,RESULT.m21,RESULT.m22,RESULT.m23);
NSLog(@" %f %f %f %f",RESULT.m30,RESULT.m31,RESULT.m32,RESULT.m33);
NSLog(@"Answer:");
NSLog(@" %f %f %f %f",ANSWER.m00,ANSWER.m01,ANSWER.m02,ANSWER.m03);
NSLog(@" %f %f %f %f",ANSWER.m10,ANSWER.m11,ANSWER.m12,ANSWER.m13);
NSLog(@" %f %f %f %f",ANSWER.m20,ANSWER.m21,ANSWER.m22,ANSWER.m23);
NSLog(@" %f %f %f %f",ANSWER.m30,ANSWER.m31,ANSWER.m32,ANSWER.m33);
NSLog(@"##################################################");
Here's the output:
##################################################
Result:
-1.000000 0.000000 0.000000 0.000000
0.000000 1.000000 0.000000 -1.000000
0.000000 0.000000 -1.000000 -1.000000
0.000000 0.000000 0.000000 1.000000
Answer:
-1.000000 0.000000 0.000000 0.000000
0.000000 1.000000 0.000000 -1.000000
0.000000 0.000000 -1.000000 1.000000
0.000000 0.000000 0.000000 1.000000
##################################################
I've spent the last 5 hours trying to debug some OpenGL code only to find this is the problem. I must be missing something, surely. Can anyone spot what's going on, or verify this shouldn't be happening?
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嗯，我得到了与你的“结果”矩阵相同的结果。
我用笔和纸进行了矩阵乘法，遵循以下规则：
http://www.mathsisfun.com/algebra/matrix-multiplying.html mathsisfun.com/algebra/matrix-multiplying.html
这就是我使用你的两个矩阵 a 和 b 所做的：
好吧，我想我知道你哪里出了问题，你一定把数字列在了错误的位置：
方式您在代码中列出的数字是水平的，例如坐标（x，y，z），但在矩阵中，这些数字被移动到垂直位置。
例如，[ XYZW ] 应该变成垂直的：
现在 IF 我们是将您的数字列出在错误的位置并将矩阵 a 与矩阵 b 相乘，我们得到与您的“答案”矩阵相同的答案：
Um, I got the same result as your "RESULT" matrix.
I did the matrix multiplication with pen and paper, following these rules:
http://www.mathsisfun.com/algebra/matrix-multiplying.html
This is how I did it using your two matrix a and b:
OK, I think I know where you went wrong, you must have listed the numbers in the wrong position:
The way you list the number in code is horizontal e.g Coordinate(x,y,z) but in a Matrix, these numbers get moved to vertical positions.
So for example, [ X Y Z W ] should become vertically:
Now IF we were to list the your numbers in the wrong position and multiply Matrix a with Matrix b, we get the same answer as your "ANSWER" matrix:
关于这一点的更多细节。
OpenGL ES 假设矩阵具有列主序。所以 OpenGL ES 读取矩阵的元素顺序是：
当然 Apple 的 GLKit Math Utilities 也是根据此列专业顺序构建的。当你意识到这一点时，可能会有点困惑。 :)
Little bit more details on this.
OpenGL ES suppose matrices have column major order. So element order how OpenGL ES reads matrix is:
Of course Apple's GLKit Math Utilities are also built according to this column majored order. And it may be little bit confusing while you realise it. :)