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m_mat.cpp
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#include "m_mat.h"
#include "m_vec.h"
#include "m_quat.h"
#ifdef __SSE2__
#include <xmmintrin.h>
#endif
namespace m {
///! mat4x4
const mat4 mat4::kIdentity({ 1.0f, 0.0f, 0.0f, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f });
mat4 mat4::identity() {
return { { 1.0f, 0.0f, 0.0f, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } };
}
mat4 mat4::scale(const vec3 &s) {
return { { s.x, 0.0f, 0.0f, 0.0f },
{ 0.0f, s.y, 0.0f, 0.0f },
{ 0.0f, 0.0f, s.z, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } };
}
mat4 mat4::rotate(const vec3 &r) {
const m::vec2 x = m::sincos(toRadian(r.x));
const m::vec2 y = m::sincos(toRadian(r.y));
const m::vec2 z = m::sincos(toRadian(r.z));
const m::mat4 rx = { { 1.0f, 0.0f, 0.0f, 0.0f },
{ 0.0f, x.y, -x.x, 0.0f },
{ 0.0f, x.x, x.y, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } },
ry = { { y.y, 0.0f, -y.x, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f },
{ y.x, 0.0f, y.y, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } },
rz = { { z.y, -z.x, 0.0f, 0.0f },
{ z.x, z.y, 0.0f, 0.0f },
{ 0.0f, 0.0f, 1.0f, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } };
return rz * ry * rx;
}
mat4 mat4::translate(const vec3 &t) {
return { { 1.0f, 0.0f, 0.0f, t.x },
{ 0.0f, 1.0f, 0.0f, t.y },
{ 0.0f, 0.0f, 1.0f, t.z },
{ 0.0f, 0.0f, 0.0f, 1.0f } };
}
mat4 mat4::lookat(const vec3 &target, const vec3 &up) {
const vec3 n = target.normalized(),
u = up.normalized().cross(n),
v = n.cross(u);
return { { u.x, u.y, u.z, 0.0f },
{ v.x, v.y, v.z, 0.0f },
{ n.x, n.y, n.z, 0.0f },
{ 0.0f, 0.0f, 0.0f, 1.0f } };
}
mat4 mat4::lookat(const vec3 &p, const quat &q) {
mat4 m;
m.a = { 1.0f - 2.0f * (q.y * q.y + q.z*q.z),
2.0f * (q.x * q.y - q.w * q.z),
2.0f * (q.x * q.z + q.w * q.y),
0.0f };
m.b = { 2.0f * (q.x * q.y + q.w * q.z),
1.0f - 2.0f * (q.x * q.x + q.z * q.z),
2.0f * (q.y * q.z - q.w * q.x),
0.0f };
m.c = { 2.0f * (q.x * q.z - q.w * q.y),
2.0f * (q.y * q.z + q.w * q.x),
1.0f - 2.0f * (q.x * q.x + q.y * q.y),
0.0f };
m.d = { -(p.x * m.a.x + p.y * m.b.x + p.z * m.c.x),
-(p.x * m.a.y + p.y * m.b.y + p.z * m.c.y),
-(p.x * m.a.z + p.y * m.b.z + p.z * m.c.z),
1.0f };
return m;
}
mat4 mat4::project(const m::perspective &p) {
const float ar = p.width / p.height;
const float range = p.nearp - p.farp;
const float halfFov = m::tan(m::toRadian(p.fov) * 0.5f);
return { { 1.0f / (halfFov * ar), 0.0f, 0.0f, 0.0f },
{ 0.0f, 1.0f / halfFov, 0.0f, 0.0f },
{ 0.0f, 0.0f, -(p.nearp + p.farp) / range, 2.0f * p.farp * p.nearp / range },
{ 0.0f, 0.0f, 1.0f, 0.0f } };
}
mat4 mat4::project(float angle, float nearClip, float farClip, float bias) {
const float halfFOV = 1.0f / m::tan(m::toRadian(angle) * 0.5f);
const float zRange = nearClip - farClip;
return { { halfFOV, 0.0f, 0.0f, 0.0f },
{ 0.0f, halfFOV, 0.0f, 0.0f },
{ 0.0f, 0.0f, -(nearClip + farClip) / zRange, 2.0f * nearClip * farClip / zRange + bias },
{ 0.0f, 0.0f, 1.0f, 0.0f} };
}
mat4 mat4::operator*(const mat4 &t) const {
return { t.a*a.splat<0>() + t.b*a.splat<1>() + t.c*a.splat<2>() + t.d*a.splat<3>(),
t.a*b.splat<0>() + t.b*b.splat<1>() + t.c*b.splat<2>() + t.d*b.splat<3>(),
t.a*c.splat<0>() + t.b*c.splat<1>() + t.c*c.splat<2>() + t.d*c.splat<3>(),
t.a*d.splat<0>() + t.b*d.splat<1>() + t.c*d.splat<2>() + t.d*d.splat<3>() };
}
#ifdef __SSE2__
mat4 mat4::inverse() const {
alignas(16) static const float kSign1[] = { 0.0f, -0.0f, 0.0f, -0.0f };
alignas(16) static const float kSign2[] = { -0.0f, 0.0f, -0.0f, 0.0f };
alignas(16) static const float kOne[] = { 1.0f, 1.0f, 1.0f, 1.0f };
const __m128 f1 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(2,2,2,2)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(3,3,3,3)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(2,2,2,2)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(3,3,3,3))));
const __m128 f2 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(1,1,1,1)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(3,3,3,3)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(1,1,1,1)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(3,3,3,3))));
const __m128 f3 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(1,1,1,1)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(2,2,2,2)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(1,1,1,1)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(2,2,2,2))));
const __m128 f4 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(0,0,0,0)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(3,3,3,3)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(0,0,0,0)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(3,3,3,3))));
const __m128 f5 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(0,0,0,0)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(2,2,2,2)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(0,0,0,0)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(2,2,2,2))));
const __m128 f6 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(0,0,0,0)),
_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(1,1,1,1)), _MM_SHUFFLE(2,0,0,0))),
_mm_mul_ps(_mm_pshufd(_mm_shuffle_ps(d.v, c.v, _MM_SHUFFLE(0,0,0,0)), _MM_SHUFFLE(2,0,0,0)),
_mm_shuffle_ps(c.v, b.v, _MM_SHUFFLE(1,1,1,1))));
const __m128 v1 = _mm_pshufd(_mm_shuffle_ps(b.v, a.v, _MM_SHUFFLE(0,0,0,0)), _MM_SHUFFLE(2,2,2,0));
const __m128 v2 = _mm_pshufd(_mm_shuffle_ps(b.v, a.v, _MM_SHUFFLE(1,1,1,1)), _MM_SHUFFLE(2,2,2,0));
const __m128 v3 = _mm_pshufd(_mm_shuffle_ps(b.v, a.v, _MM_SHUFFLE(2,2,2,2)), _MM_SHUFFLE(2,2,2,0));
const __m128 v4 = _mm_pshufd(_mm_shuffle_ps(b.v, a.v, _MM_SHUFFLE(3,3,3,3)), _MM_SHUFFLE(2,2,2,0));
const __m128 s1 = *(const __m128 *)kSign1;
const __m128 s2 = *(const __m128 *)kSign2;
const __m128 i1 = _mm_xor_ps(s1, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v2, f1),
_mm_mul_ps(v3, f2)),
_mm_mul_ps(v4, f3)));
const __m128 i2 = _mm_xor_ps(s2, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f1),
_mm_mul_ps(v3, f4)),
_mm_mul_ps(v4, f5)));
const __m128 i3 = _mm_xor_ps(s1, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f2),
_mm_mul_ps(v2, f4)),
_mm_mul_ps(v4, f6)));
const __m128 i4 = _mm_xor_ps(s2, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f3),
_mm_mul_ps(v2, f5)),
_mm_mul_ps(v3, f6)));
const __m128 d0 = _mm_mul_ps(a.v, _mm_movelh_ps(_mm_unpacklo_ps(i1, i2),
_mm_unpacklo_ps(i3, i4)));
const __m128 d1 = _mm_add_ps(d0, _mm_pshufd(d0, _MM_SHUFFLE(1,0,3,2)));
const __m128 d2 = _mm_add_ps(d1, _mm_pshufd(d1, _MM_SHUFFLE(0,1,0,1)));
const __m128 d3 = _mm_div_ps(*(const __m128 *)kOne, d2);
return { _mm_mul_ps(i1, d3), _mm_mul_ps(i2, d3), _mm_mul_ps(i3, d3), _mm_mul_ps(i4, d3) };
}
#else
inline float mat4::det2x2(float a, float b, float c, float d) {
return a*d - b*c;
}
inline float mat4::det3x3(float a1, float a2, float a3,
float b1, float b2, float b3,
float c1, float c2, float c3)
{
return a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3);
}
mat4 mat4::inverse() const {
mat4 m;
const float a1 = a.x, a2 = a.y, a3 = a.z, a4 = a.w,
b1 = b.x, b2 = b.y, b3 = b.z, b4 = b.w,
c1 = c.x, c2 = c.y, c3 = c.z, c4 = c.w,
d1 = d.x, d2 = d.y, d3 = d.z, d4 = d.w,
v1 = det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4),
v2 = -det3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4),
v3 = det3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4),
v4 = -det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4),
nd = a1*v1 + b1*v2 + c1*v3 + d1*v4,
id = 1.0f / nd;
m.a.x = v1 * id;
m.a.y = v2 * id;
m.a.z = v3 * id;
m.a.w = v4 * id;
m.b.x = -det3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4) * id;
m.b.y = det3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4) * id;
m.b.z = -det3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4) * id;
m.b.w = det3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4) * id;
m.c.x = det3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4) * id;
m.c.y = -det3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4) * id;
m.c.z = det3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4) * id;
m.c.w = -det3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4) * id;
m.d.x = -det3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3) * id;
m.d.y = det3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3) * id;
m.d.z = -det3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3) * id;
m.d.w = det3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3) * id;
return m;
}
#endif
///! mat3x3
void mat3x3::convertQuaternion(const quat &q) {
const float x = q.x;
const float y = q.y;
const float z = q.z;
const float w = q.w;
const float tx = 2*x;
const float ty = 2*y;
const float tz = 2*z;
const float txx = tx*x;
const float tyy = ty*y;
const float tzz = tz*z;
const float txy = tx*y;
const float txz = tx*z;
const float tyz = ty*z;
const float twx = w*tx;
const float twy = w*ty;
const float twz = w*tz;
a = { 1 - (tyy + tzz), txy - twz, txz + twy };
b = { txy + twz, 1 - (txx + tzz), tyz - twx };
c = { txz - twy, tyz + twx, 1 - (txx + tyy) };
}
///! mat3x4
void mat3x4::invert(const mat3x4 &o) {
mat3x3 inv(vec3(o.a.x, o.b.x, o.c.x),
vec3(o.a.y, o.b.y, o.c.y),
vec3(o.a.z, o.b.z, o.c.z));
inv.a /= (inv.a * inv.a);
inv.b /= (inv.b * inv.b);
inv.c /= (inv.c * inv.c);
const vec3 trans(o.a.w, o.b.w, o.c.w);
a = vec4(inv.a, -inv.a*trans);
b = vec4(inv.b, -inv.b*trans);
c = vec4(inv.c, -inv.c*trans);
}
}