384 lines
9.0 KiB
C++
Executable File
384 lines
9.0 KiB
C++
Executable File
#include "Math.h"
|
|
|
|
#include <exception>
|
|
|
|
namespace ZL {
|
|
|
|
Vector2f operator+(const Vector2f& x, const Vector2f& y)
|
|
{
|
|
Vector2f result;
|
|
|
|
result.v[0] = x.v[0] + y.v[0];
|
|
result.v[1] = x.v[1] + y.v[1];
|
|
|
|
return result;
|
|
}
|
|
|
|
Vector2f operator-(const Vector2f& x, const Vector2f& y)
|
|
{
|
|
Vector2f result;
|
|
|
|
result.v[0] = x.v[0] - y.v[0];
|
|
result.v[1] = x.v[1] - y.v[1];
|
|
|
|
return result;
|
|
}
|
|
|
|
Matrix3f Matrix3f::Identity()
|
|
{
|
|
Matrix3f r;
|
|
|
|
r.m[0] = 1.f;
|
|
r.m[1] = 0.f;
|
|
r.m[2] = 0.f;
|
|
|
|
r.m[3] = 0.f;
|
|
r.m[4] = 1.f;
|
|
r.m[5] = 0.f;
|
|
|
|
r.m[6] = 0.f;
|
|
r.m[7] = 0.f;
|
|
r.m[8] = 1.f;
|
|
|
|
return r;
|
|
|
|
}
|
|
|
|
Matrix4f Matrix4f::Identity()
|
|
{
|
|
Matrix4f r;
|
|
|
|
r.m[0] = 1.f;
|
|
r.m[1] = 0.f;
|
|
r.m[2] = 0.f;
|
|
r.m[3] = 0.f;
|
|
|
|
r.m[4] = 0.f;
|
|
r.m[5] = 1.f;
|
|
r.m[6] = 0.f;
|
|
r.m[7] = 0.f;
|
|
|
|
r.m[8] = 0.f;
|
|
r.m[9] = 0.f;
|
|
r.m[10] = 1.f;
|
|
r.m[11] = 0.f;
|
|
|
|
r.m[12] = 0.f;
|
|
r.m[13] = 0.f;
|
|
r.m[14] = 0.f;
|
|
r.m[15] = 1.f;
|
|
|
|
return r;
|
|
|
|
}
|
|
|
|
Matrix4f operator*(const Matrix4f& m1, const Matrix4f& m2)
|
|
{
|
|
Matrix4f r;
|
|
|
|
r.m[0] = m1.m[0] * m2.m[0] + m1.m[4] * m2.m[1] + m1.m[8] * m2.m[2] + m1.m[12] * m2.m[3];
|
|
r.m[1] = m1.m[1] * m2.m[0] + m1.m[5] * m2.m[1] + m1.m[9] * m2.m[2] + m1.m[13] * m2.m[3];
|
|
r.m[2] = m1.m[2] * m2.m[0] + m1.m[6] * m2.m[1] + m1.m[10] * m2.m[2] + m1.m[14] * m2.m[3];
|
|
r.m[3] = m1.m[3] * m2.m[0] + m1.m[7] * m2.m[1] + m1.m[11] * m2.m[2] + m1.m[15] * m2.m[3];
|
|
|
|
r.m[4] = m1.m[0] * m2.m[4] + m1.m[4] * m2.m[5] + m1.m[8] * m2.m[6] + m1.m[12] * m2.m[7];
|
|
r.m[5] = m1.m[1] * m2.m[4] + m1.m[5] * m2.m[5] + m1.m[9] * m2.m[6] + m1.m[13] * m2.m[7];
|
|
r.m[6] = m1.m[2] * m2.m[4] + m1.m[6] * m2.m[5] + m1.m[10] * m2.m[6] + m1.m[14] * m2.m[7];
|
|
r.m[7] = m1.m[3] * m2.m[4] + m1.m[7] * m2.m[5] + m1.m[11] * m2.m[6] + m1.m[15] * m2.m[7];
|
|
|
|
|
|
r.m[8] = m1.m[0] * m2.m[8] + m1.m[4] * m2.m[9] + m1.m[8] * m2.m[10] + m1.m[12] * m2.m[11];
|
|
r.m[9] = m1.m[1] * m2.m[8] + m1.m[5] * m2.m[9] + m1.m[9] * m2.m[10] + m1.m[13] * m2.m[11];
|
|
r.m[10] = m1.m[2] * m2.m[8] + m1.m[6] * m2.m[9] + m1.m[10] * m2.m[10] + m1.m[14] * m2.m[11];
|
|
r.m[11] = m1.m[3] * m2.m[8] + m1.m[7] * m2.m[9] + m1.m[11] * m2.m[10] + m1.m[15] * m2.m[11];
|
|
|
|
r.m[12] = m1.m[0] * m2.m[12] + m1.m[4] * m2.m[13] + m1.m[8] * m2.m[14] + m1.m[12] * m2.m[15];
|
|
r.m[13] = m1.m[1] * m2.m[12] + m1.m[5] * m2.m[13] + m1.m[9] * m2.m[14] + m1.m[13] * m2.m[15];
|
|
r.m[14] = m1.m[2] * m2.m[12] + m1.m[6] * m2.m[13] + m1.m[10] * m2.m[14] + m1.m[14] * m2.m[15];
|
|
r.m[15] = m1.m[3] * m2.m[12] + m1.m[7] * m2.m[13] + m1.m[11] * m2.m[14] + m1.m[15] * m2.m[15];
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix4f MakeOrthoMatrix(float width, float height, float zNear, float zFar)
|
|
{
|
|
float depthRange = zFar - zNear;
|
|
|
|
if (depthRange <= 0)
|
|
{
|
|
throw std::runtime_error("zFar must be greater than zNear");
|
|
}
|
|
|
|
Matrix4f r;
|
|
|
|
r.m[0] = 2.f / width;
|
|
r.m[1] = 0;
|
|
r.m[2] = 0;
|
|
r.m[3] = 0;
|
|
|
|
r.m[4] = 0;
|
|
r.m[5] = 2.f / height;
|
|
r.m[6] = 0;
|
|
r.m[7] = 0;
|
|
|
|
r.m[8] = 0;
|
|
r.m[9] = 0;
|
|
r.m[10] = -1 / depthRange;
|
|
r.m[11] = 0;
|
|
|
|
r.m[12] = -1;
|
|
r.m[13] = -1;
|
|
r.m[14] = zNear / depthRange;
|
|
r.m[15] = 1;
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix4f MakePerspectiveMatrix(float fovY, float aspectRatio, float zNear, float zFar)
|
|
{
|
|
float tanHalfFovy = tan(fovY / 2.f);
|
|
Matrix4f r;
|
|
|
|
if (zNear >= zFar || aspectRatio == 0)
|
|
{
|
|
throw std::runtime_error("Invalid perspective parameters");
|
|
}
|
|
|
|
r.m[0] = 1.f / (aspectRatio * tanHalfFovy);
|
|
r.m[1] = 0;
|
|
r.m[2] = 0;
|
|
r.m[3] = 0;
|
|
|
|
r.m[4] = 0;
|
|
r.m[5] = 1.f / (tanHalfFovy);
|
|
r.m[6] = 0;
|
|
r.m[7] = 0;
|
|
|
|
r.m[8] = 0;
|
|
r.m[9] = 0;
|
|
r.m[10] = -(zFar + zNear) / (zFar - zNear);
|
|
r.m[11] = -1;
|
|
|
|
r.m[12] = 0;
|
|
r.m[13] = 0;
|
|
r.m[14] = -(2.f * zFar * zNear) / (zFar - zNear);
|
|
r.m[15] = 0;
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix3f QuatToMatrix(const Vector4f& q)
|
|
{
|
|
Matrix3f m;
|
|
|
|
float wx, wy, wz, xx, yy, yz, xy, xz, zz, s, x2, y2, z2;
|
|
|
|
s = 2.0f / (q.v[0] * q.v[0] + q.v[1] * q.v[1] + q.v[2] * q.v[2] + q.v[3] * q.v[3]);
|
|
|
|
|
|
x2 = q.v[0] * s;
|
|
y2 = q.v[1] * s;
|
|
z2 = q.v[2] * s;
|
|
|
|
wx = q.v[3] * x2; wy = q.v[3] * y2; wz = q.v[3] * z2;
|
|
xx = q.v[0] * x2; xy = q.v[1] * x2; xz = q.v[2] * x2;
|
|
yy = q.v[1] * y2; yz = q.v[2] * y2;
|
|
zz = q.v[2] * z2;
|
|
|
|
m.m[0] = 1.0f - (yy + zz);
|
|
m.m[1] = xy + wz;
|
|
m.m[2] = xz - wy;
|
|
|
|
m.m[3] = xy - wz;
|
|
m.m[4] = 1.0f - (xx + zz);
|
|
m.m[5] = yz + wx;
|
|
|
|
m.m[6] = xz + wy;
|
|
m.m[7] = yz - wx;
|
|
m.m[8] = 1.0f - (xx + yy);
|
|
|
|
return m;
|
|
|
|
}
|
|
|
|
Vector4f QuatFromRotateAroundX(float angle)
|
|
{
|
|
Vector4f result;
|
|
|
|
result.v[0] = sinf(angle * 0.5f);
|
|
result.v[1] = 0.f;
|
|
result.v[2] = 0.f;
|
|
result.v[3] = cosf(angle * 0.5f);
|
|
|
|
return result;
|
|
}
|
|
|
|
Vector4f QuatFromRotateAroundY(float angle)
|
|
{
|
|
Vector4f result;
|
|
|
|
result.v[0] = 0.f;
|
|
result.v[1] = sinf(angle * 0.5f);
|
|
result.v[2] = 0.f;
|
|
result.v[3] = cosf(angle * 0.5f);
|
|
|
|
return result;
|
|
}
|
|
|
|
Vector4f QuatFromRotateAroundZ(float angle)
|
|
{
|
|
Vector4f result;
|
|
|
|
result.v[0] = 0.f;
|
|
result.v[1] = 0.f;
|
|
result.v[2] = sinf(angle * 0.5f);
|
|
result.v[3] = cosf(angle * 0.5f);
|
|
|
|
return result;
|
|
}
|
|
|
|
Matrix3f TransposeMatrix(const Matrix3f& m)
|
|
{
|
|
Matrix3f r;
|
|
r.m[0] = m.m[0];
|
|
r.m[1] = m.m[3];
|
|
r.m[2] = m.m[6];
|
|
r.m[3] = m.m[1];
|
|
r.m[4] = m.m[4];
|
|
r.m[5] = m.m[7];
|
|
r.m[6] = m.m[2];
|
|
r.m[7] = m.m[5];
|
|
r.m[8] = m.m[8];
|
|
return r;
|
|
}
|
|
|
|
Matrix3f InverseMatrix(const Matrix3f& m)
|
|
{
|
|
float d;
|
|
Matrix3f r;
|
|
|
|
d = m.m[0] * (m.m[4] * m.m[8] - m.m[5] * m.m[7]);
|
|
d -= m.m[1] * (m.m[3] * m.m[8] - m.m[6] * m.m[5]);
|
|
d += m.m[2] * (m.m[3] * m.m[7] - m.m[6] * m.m[4]);
|
|
|
|
if (fabs(d) < 0.01f)
|
|
{
|
|
throw std::runtime_error("Error: matrix cannot be inversed!");
|
|
|
|
}
|
|
else
|
|
{
|
|
|
|
r.m[0] = (m.m[4] * m.m[8] - m.m[5] * m.m[7]) / d;
|
|
r.m[1] = -(m.m[1] * m.m[8] - m.m[2] * m.m[7]) / d;
|
|
r.m[2] = (m.m[1] * m.m[5] - m.m[2] * m.m[4]) / d;
|
|
|
|
r.m[3] = -(m.m[3] * m.m[8] - m.m[5] * m.m[6]) / d;
|
|
r.m[4] = (m.m[0] * m.m[8] - m.m[2] * m.m[6]) / d;
|
|
r.m[5] = -(m.m[0] * m.m[5] - m.m[2] * m.m[3]) / d;
|
|
|
|
r.m[6] = (m.m[3] * m.m[7] - m.m[6] * m.m[4]) / d;
|
|
r.m[7] = -(m.m[0] * m.m[7] - m.m[6] * m.m[1]) / d;
|
|
r.m[8] = (m.m[0] * m.m[4] - m.m[1] * m.m[3]) / d;
|
|
|
|
};
|
|
return r;
|
|
}
|
|
|
|
Matrix3f CreateZRotationMatrix(float angle)
|
|
{
|
|
Matrix3f result = Matrix3f::Identity();
|
|
|
|
result.m[0] = cosf(angle);
|
|
result.m[1] = -sinf(angle);
|
|
result.m[3] = sinf(angle);
|
|
result.m[4] = cosf(angle);
|
|
|
|
return result;
|
|
}
|
|
|
|
Matrix4f MultMatrixMatrix(const Matrix4f& m1, const Matrix4f& m2)
|
|
{
|
|
Matrix4f r;
|
|
|
|
r.m[0] = m1.m[0] * m2.m[0] + m1.m[4] * m2.m[1] + m1.m[8] * m2.m[2] + m1.m[12] * m2.m[3];
|
|
r.m[1] = m1.m[1] * m2.m[0] + m1.m[5] * m2.m[1] + m1.m[9] * m2.m[2] + m1.m[13] * m2.m[3];
|
|
r.m[2] = m1.m[2] * m2.m[0] + m1.m[6] * m2.m[1] + m1.m[10] * m2.m[2] + m1.m[14] * m2.m[3];
|
|
r.m[3] = m1.m[3] * m2.m[0] + m1.m[7] * m2.m[1] + m1.m[11] * m2.m[2] + m1.m[15] * m2.m[3];
|
|
|
|
r.m[4] = m1.m[0] * m2.m[4] + m1.m[4] * m2.m[5] + m1.m[8] * m2.m[6] + m1.m[12] * m2.m[7];
|
|
r.m[5] = m1.m[1] * m2.m[4] + m1.m[5] * m2.m[5] + m1.m[9] * m2.m[6] + m1.m[13] * m2.m[7];
|
|
r.m[6] = m1.m[2] * m2.m[4] + m1.m[6] * m2.m[5] + m1.m[10] * m2.m[6] + m1.m[14] * m2.m[7];
|
|
r.m[7] = m1.m[3] * m2.m[4] + m1.m[7] * m2.m[5] + m1.m[11] * m2.m[6] + m1.m[15] * m2.m[7];
|
|
|
|
|
|
r.m[8] = m1.m[0] * m2.m[8] + m1.m[4] * m2.m[9] + m1.m[8] * m2.m[10] + m1.m[12] * m2.m[11];
|
|
r.m[9] = m1.m[1] * m2.m[8] + m1.m[5] * m2.m[9] + m1.m[9] * m2.m[10] + m1.m[13] * m2.m[11];
|
|
r.m[10] = m1.m[2] * m2.m[8] + m1.m[6] * m2.m[9] + m1.m[10] * m2.m[10] + m1.m[14] * m2.m[11];
|
|
r.m[11] = m1.m[3] * m2.m[8] + m1.m[7] * m2.m[9] + m1.m[11] * m2.m[10] + m1.m[15] * m2.m[11];
|
|
|
|
r.m[12] = m1.m[0] * m2.m[12] + m1.m[4] * m2.m[13] + m1.m[8] * m2.m[14] + m1.m[12] * m2.m[15];
|
|
r.m[13] = m1.m[1] * m2.m[12] + m1.m[5] * m2.m[13] + m1.m[9] * m2.m[14] + m1.m[13] * m2.m[15];
|
|
r.m[14] = m1.m[2] * m2.m[12] + m1.m[6] * m2.m[13] + m1.m[10] * m2.m[14] + m1.m[14] * m2.m[15];
|
|
r.m[15] = m1.m[3] * m2.m[12] + m1.m[7] * m2.m[13] + m1.m[11] * m2.m[14] + m1.m[15] * m2.m[15];
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix3f MakeTranslationMatrix(const Vector3f& p)
|
|
{
|
|
Matrix3f r = Matrix3f::Identity();
|
|
|
|
r.m[12] = p.v[0];
|
|
r.m[13] = p.v[1];
|
|
r.m[14] = p.v[2];
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix3f MakeScaleMatrix(float scale)
|
|
{
|
|
Matrix3f r = Matrix3f::Identity();
|
|
|
|
r.m[0] = scale;
|
|
r.m[5] = scale;
|
|
r.m[10] = scale;
|
|
|
|
return r;
|
|
}
|
|
|
|
Matrix3f MakeRotationMatrix(const Vector3f& p)
|
|
{
|
|
Matrix3f r = Matrix3f::Identity();
|
|
|
|
r.m[12] = p.v[0];
|
|
r.m[13] = p.v[1];
|
|
r.m[14] = p.v[2];
|
|
|
|
return r;
|
|
}
|
|
|
|
Vector3f operator*(Vector3f v, float scale)
|
|
{
|
|
Vector3f r = v;
|
|
|
|
r.v[0] = v.v[0] * scale;
|
|
r.v[1] = v.v[1] * scale;
|
|
r.v[2] = v.v[2] * scale;
|
|
|
|
return r;
|
|
}
|
|
|
|
Vector3f MultVectorMatrix(Vector3f v, Matrix3f mt)
|
|
{
|
|
Vector3f r;
|
|
|
|
r.v[0] = v.v[0] * mt.m[0] + v.v[1] * mt.m[1] + v.v[2] * mt.m[2];
|
|
r.v[1] = v.v[0] * mt.m[3] + v.v[1] * mt.m[4] + v.v[2] * mt.m[5];
|
|
r.v[2] = v.v[0] * mt.m[6] + v.v[1] * mt.m[7] + v.v[2] * mt.m[8];
|
|
|
|
return r;
|
|
}
|
|
|
|
};
|