OpenGL中两种计算投影矩阵的函数
OpenGL无意间同时看到两种创建投影矩阵的写法,可以说它们完成的是同样的功能,但写法完全不同,可以观摩一下什么叫做异曲同工之妙...
第一种:
gltMakeShadowMatrix函数是重点
1 // Gets the three coefficients of a plane equation given three points on the plane. 2 void gltGetPlaneEquation(GLTVector3 vPoint1, GLTVector3 vPoint2, GLTVector3 vPoint3, GLTVector3 vPlane) 3 { 4 // Get normal vector from three points. The normal vector is the first three coefficients 5 // to the plane equation... 6 gltGetNormalVector(vPoint1, vPoint2, vPoint3, vPlane); 7 8 // Final coefficient found by back substitution 9 vPlane[3] = -(vPlane[0] * vPoint3[0] + vPlane[1] * vPoint3[1] + vPlane[2] * vPoint3[2]); 10 } 11 12 void gltMakeShadowMatrix(GLTVector3 vPoints[3], GLTVector4 vLightPos, GLTMatrix destMat) 13 { 14 GLTVector4 vPlaneEquation; 15 GLfloat dot; 16 17 gltGetPlaneEquation(vPoints[0], vPoints[1], vPoints[2], vPlaneEquation); 18 19 // Dot product of plane and light position 20 dot = vPlaneEquation[0]*vLightPos[0] + 21 vPlaneEquation[1]*vLightPos[1] + 22 vPlaneEquation[2]*vLightPos[2] + 23 vPlaneEquation[3]*vLightPos[3]; 24 25 26 // Now do the projection 27 // First column 28 destMat[0] = dot - vLightPos[0] * vPlaneEquation[0]; 29 destMat[4] = 0.0f - vLightPos[0] * vPlaneEquation[1]; 30 destMat[8] = 0.0f - vLightPos[0] * vPlaneEquation[2]; 31 destMat[12] = 0.0f - vLightPos[0] * vPlaneEquation[3]; 32 33 // Second column 34 destMat[1] = 0.0f - vLightPos[1] * vPlaneEquation[0]; 35 destMat[5] = dot - vLightPos[1] * vPlaneEquation[1]; 36 destMat[9] = 0.0f - vLightPos[1] * vPlaneEquation[2]; 37 destMat[13] = 0.0f - vLightPos[1] * vPlaneEquation[3]; 38 39 // Third Column 40 destMat[2] = 0.0f - vLightPos[2] * vPlaneEquation[0]; 41 destMat[6] = 0.0f - vLightPos[2] * vPlaneEquation[1]; 42 destMat[10] = dot - vLightPos[2] * vPlaneEquation[2]; 43 destMat[14] = 0.0f - vLightPos[2] * vPlaneEquation[3]; 44 45 // Fourth Column 46 destMat[3] = 0.0f - vLightPos[3] * vPlaneEquation[0]; 47 destMat[7] = 0.0f - vLightPos[3] * vPlaneEquation[1]; 48 destMat[11] = 0.0f - vLightPos[3] * vPlaneEquation[2]; 49 destMat[15] = dot - vLightPos[3] * vPlaneEquation[3]; 50 }
1 // Given three points on a plane in counter clockwise order, calculate the unit normal 2 void gltGetNormalVector(const GLTVector3 vP1, const GLTVector3 vP2, const GLTVector3 vP3, GLTVector3 vNormal) 3 { 4 GLTVector3 vV1, vV2; 5 6 gltSubtractVectors(vP2, vP1, vV1); 7 gltSubtractVectors(vP3, vP1, vV2); 8 9 gltVectorCrossProduct(vV1, vV2, vNormal); 10 gltNormalizeVector(vNormal); 11 }
第二种:
CreateShadowMatrix函数是重点
1 第二种 2 /** 创建投射矩阵 */ 3 void CPlanarShadow::CreateShadowMatrix(float m[16], Vector3 point, Vector3 normal, float lp[4]) 4 { 5 /** 计算顶点到平面的距离 */ 6 float d = - ((normal.x * point.x) + (normal.y * point.y) + (normal.z * point.z)); 7 8 /** 计算光源向量和法向量的点积 */ 9 float dot = normal.x*lp[0] + normal.y*lp[1] + normal.z*lp[2] + d*lp[3]; 10 11 /** 设置矩阵元素值 */ 12 m[0] = dot - lp[0]*normal.x; m[1] = -lp[1]*normal.x; m[2] = -lp[2]*normal.x; m[3] = -lp[3]*normal.x; 13 m[4] = -lp[0]*normal.y; m[5] = dot -lp[1]*normal.y; m[6] = -lp[2]*normal.y; m[7] = -lp[3]*normal.y; 14 m[8] = -lp[0]*normal.z; m[9] = -lp[1]*normal.z; m[10] = dot - lp[2]*normal.z; m[11] = -lp[3]*normal.z; 15 m[12] = -lp[0]*d; m[13] = -lp[1]*d; m[14] = -lp[2]*d; m[15] = dot -lp[3]*d; 16 }
