概述

計算OpenGL的正交投影矩陣和透視投影矩陣是有現成函數的。自己手推不是為了重復造輪子。手推一遍，可以極大的加強對這兩個矩陣的理解。同時也可以滿足一下自己求知欲。

正交投影矩陣手推

正交投影矩陣源碼

WGMatrix4x4 WGMatrix4x4::BuildOrtho(double l, double r, double b, double t, double n, double f) {WGMatrix4x4 matrix;double w = r - l;double h = t - b;double d = f - n;matrix.m_elements[0][0] = 2 / w;matrix.m_elements[0][1] = 0;matrix.m_elements[0][2] = 0;matrix.m_elements[0][3] = -(r + l) / w;matrix.m_elements[1][0] = 0;matrix.m_elements[1][1] = 2 / h;matrix.m_elements[1][2] = 0;matrix.m_elements[1][3] = -(t + b) / h;matrix.m_elements[2][0] = 0;matrix.m_elements[2][1] = 0;matrix.m_elements[2][2] = -2 / d;matrix.m_elements[2][3] = -(f + n) / d;matrix.m_elements[3][0] = 0;matrix.m_elements[3][1] = 0;matrix.m_elements[3][2] = 0;matrix.m_elements[3][3] = 1;matrix.m_type = WGMatrix4x4Type::TRS;return matrix;
}

透視投影矩陣手推

透視投影矩陣源碼

WGMatrix4x4 WGMatrix4x4::BuildFrustum(double l, double r, double b, double t, double n, double f) {WGMatrix4x4 matrix;double w = r - l;double h = t - b;double d = f - n;matrix.m_elements[0][0] = 2 * n / w;matrix.m_elements[0][1] = 0;matrix.m_elements[0][2] = (r + l) / w;matrix.m_elements[0][3] = 0;matrix.m_elements[1][0] = 0;matrix.m_elements[1][1] = 2 * n / h;matrix.m_elements[1][2] = (t + b) / h;matrix.m_elements[1][3] = 0;matrix.m_elements[2][0] = 0;matrix.m_elements[2][1] = 0;matrix.m_elements[2][2] = -(f + n) / d;matrix.m_elements[2][3] = -2 * f * n / d;matrix.m_elements[3][0] = 0;matrix.m_elements[3][1] = 0;matrix.m_elements[3][2] = -1;matrix.m_elements[3][3] = 0;matrix.m_type = WGMatrix4x4Type::Unknown;return matrix;
}