透视投影和视图矩阵:深度缓冲区和三角形面的方向在OpenGL中都相反 [英] Perspective projection and view matrix: Both depth buffer and triangle face orientation are reversed in OpenGL
问题描述
我在OpenGL中的场景遇到了麻烦.应该将更远的对象拉近一些，以此类推，并剔除正面的三角形，而不是背面的三角形.它们以正确的方向绘制，因为它是我以前使用过的包装.我坚信这与我的投影或veiwModel矩阵有关.我看不到这些有什么问题！
I am having trouble with my scene in OpenGL. Objects that are supposed to be further away are drawn closer etc AND front facing triangles are being culled instead of back facing ones. They are drawn in the correct orientation as it is a package I have used before. I am convinced that it is something to do with my projection or veiwModel matrix. I can not see anything wrong with these though!
AV4X4FLOAT formProjMatrix(float FOVangle,float aspect,float nearz,float farz)
{
AV4X4FLOAT A;
A.m[0] = 1/(aspect*tanf(FOVangle/2));
A.m[5] = 1/tanf(FOVangle/2);
A.m[10] = farz/(farz-nearz);
A.m[11] = -nearz*farz/(farz-nearz);
A.m[14] = 1;
return A;
}
AV4X4FLOAT formViewModelMatrix(AV4FLOAT pos,AV4FLOAT target,AV4FLOAT up)
{
AV4X4FLOAT M;
AV4X4FLOAT R;
AV4FLOAT u;
AV4FLOAT v;
AV4FLOAT W;
W.x = -pos.x + target.x;
W.y = -pos.y + target.y;
W.z = -pos.z + target.z;
W.w = 0;
W.normalize();
u.x = up.y*W.z-W.y*up.z;
u.y = -up.x*W.z+W.x*up.z;
u.z = up.x*W.y-W.x*up.y;
u.w = 0;
u.normalize();
v.x = W.y*u.z-u.y*W.z;
v.y = -W.x*u.z+u.x*W.z;
v.z = W.x*u.y-u.x*W.y;
v.w = 0;
M.m[0] = u.x; M.m[1] = u.y; M.m[2] = u.z; M.m[3] = 0;
M.m[4] = v.x; M.m[5] = v.y; M.m[6] = v.z; M.m[7] = 0;
M.m[8] = -W.x; M.m[9] = -W.y; M.m[10] = -W.z; M.m[11] = 0;
M.m[12] = 0; M.m[13] = 0; M.m[14] = 0; M.m[15] = 1;
R.m[0] = 1;
R.m[5] = 1;
R.m[10] = 1;
R.m[15] = 1;
R.m[12] = -pos.x;
R.m[13] = -pos.y;
R.m[14] = -pos.z;
//the opposite of what you expect because of the way we overload mult operator!
M.display ();
R.display ();
return M*R;
}
这就是我在绘图程序中所说的.
This is what I call in my drawing routine.
glMatrixMode(GL_PROJECTION);
glLoadMatrixf(projMatrix.m);
glMatrixMode(GL_MODELVIEW);
glLoadMatrixf(viewModelMatrix.m);
一些其他信息，
是的，我已启用深度测试！
Yes, I have enabled depth testing!
推荐答案
投影矩阵的计算存在一些问题.您必须像这样修改代码:
There are some issues with in the calculation of the projection matrix. You have to adapt your code like this:
AV4X4FLOAT formProjMatrix(float FOVangle,float aspect,float nearz,float farz)
{
AV4X4FLOAT A;
A.m[0] = 1.0 / (aspect*tanf(FOVangle/2));
A.m[5] = 1.0 / tanf(FOVangle/2);
A.m[10] = (nearz+farz)/(farz-nearz);
A.m[11] = - 2.0 * nearz*farz/(farz-nearz);
A.m[14] = - 1.0;
return A;
}
透视投影矩阵如下:
r = right, l = left, b = bottom, t = top, n = near, f = far
2*n/(r-l) 0 0 0
0 2*n/(t-b) 0 0
(r+l)/(r-l) (t+b)/(t-b) -(f+n)/(f-n) -1
0 0 -2*f*n/(f-n) 0
它遵循:
aspect = w / h
tanFov = tan( fov_y * 0.5 );
p[0][0] = 2*n/(r-l) = 1.0 / (tanFov * aspect)
p[1][1] = 2*n/(t-b) = 1.0 / tanFov
以下函数将计算与gluPerspective或glm::perspective相同的投影矩阵:
The following function will calculate the same projection matrix as gluPerspective or glm::perspective does:
#include <array>
const float cPI = 3.14159265f;
float ToRad( float deg ) { return deg * cPI / 180.0f; }
using TVec4 = std::array< float, 4 >;
using TMat44 = std::array< TVec4, 4 >;
TMat44 Perspective( float fov_y, float aspect )
{
float fn = far + near
float f_n = far - near;
float r = aspect;
float t = 1.0f / tan( ToRad( fov_y ) / 2.0f );
return TMat44{
TVec4{ t / r, 0.0f, 0.0f, 0.0f },
TVec4{ 0.0f, t, 0.0f, 0.0f },
TVec4{ 0.0f, 0.0f, -fn / f_n, -1.0f },
TVec4{ 0.0f, 0.0f, -2.0f*far*near / f_n, 0.0f }
};
}
在视口上，X轴指向左侧，Y轴指向上方，Z轴指向视图之外(请注意，在右手系统中，Z轴是X轴与Y-轴的叉积轴).
On the viewport the X-axis points to the left, the Y-axis up and the Z-axis out of the view (Note in a right hand system the Z-Axis is the cross product of the X-Axis and the Y-Axis).
以下代码与gluLookAt或glm::lookAt相同:
using TVec3 = std::array< float, 3 >;
using TVec4 = std::array< float, 4 >;
using TMat44 = std::array< TVec4, 4 >;
TVec3 Cross( TVec3 a, TVec3 b ) { return { a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0] }; }
float Dot( TVec3 a, TVec3 b ) { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; }
void Normalize( TVec3 & v )
{
float len = sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
v[0] /= len; v[1] /= len; v[2] /= len;
}
TMat44 Camera::LookAt( const TVec3 &pos, const TVec3 &target, const TVec3 &up )
{
TVec3 mz = { pos[0] - target[0], pos[1] - target[1], pos[2] - target[2] };
Normalize( mz );
TVec3 my = { up[0], up[1], up[2] };
TVec3 mx = Cross( my, mz );
Normalize( mx );
my = Cross( mz, mx );
TMat44 v{
TVec4{ mx[0], my[0], mz[0], 0.0f },
TVec4{ mx[1], my[1], mz[1], 0.0f },
TVec4{ mx[2], my[2], mz[2], 0.0f },
TVec4{ Dot(mx, pos), Dot(my, pos), -Dot(mz, pos), 1.0f }
};
return v;
}
像这样修改您的代码:
AV4X4FLOAT formViewModelMatrix(AV4FLOAT pos,AV4FLOAT target,AV4FLOAT up)
{
AV4FLOAT mz;
mz.x = pos.x - target.x; mz.y = pos.y - target.y; mz.z = pos.z - target.z; mz.w = 1.0f;
mz.normalize();
AV4FLOAT my;
my.x = up.x; my.y = up.y; my.z = up.z; my.w = 1.0f;
AV4FLOAT mx;
mx.x = my.y*mz.z - my.z*mz.y; mx.y = my.z*mz.x - my.x*mz.z; mx.z = my.x*mz.y - my.y*mz.x; mx.w = 1.0f;
mx.normylize();
my.x = mz.y*mx.z - mz.z*mx.y; my.y = mz.z*mx.x - mz.x*mx.z; my.z = mz.x*mx.y - mz.y*mx.x; my.w = 1.0f;
AV4FLOAT t;
t.x = mx.x*pos.x + mx.y*pos.y + mx.z*pos.z;
t.y = my.x*pos.x + my.y*pos.y + my.z*pos.z;
t.z = -(mz.x*pos.x + mz.y*pos.y + mz.z*pos.z);
AV4X4FLOAT m;
m[0] = mx.x; m[1] = my.x; m[2] = mz.x; m[3] = 0.0f;
m[4] = mx.y; m[5] = my.y; m[6] = mz.y; m[7] = 0.0f;
m[8] = mx.z; m[9] = my.z; m[10] = mz.z; m[11] = 0.0f;
m[12] = t.x; m[13] = t.y; m[14] = t.z; m[15] = 1.0f;
return m
}
进一步了解以下问题的答案:
See further the answers to the following question:
- How to render depth linearly in modern OpenGL with gl_FragCoord.z in fragment shader?
- How to recover view space position given view space depth value and ndc xy
- Transform the modelMatrix
- Stretching Issue with Custom View Matrix
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