rendering-in-cgi/Framework/external/embree/tutorials/common/math/linearspace.isph
2024-04-23 10:14:24 +02:00

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// Copyright 2009-2021 Intel Corporation
// SPDX-License-Identifier: Apache-2.0
#pragma once
#include "vec.isph"
#include "quaternion.isph"
struct LinearSpace3f
{
Vec3f vx;
Vec3f vy;
Vec3f vz;
};
struct LinearSpace3fa
{
Vec3fa vx;
Vec3fa vy;
Vec3fa vz;
};
////////////////////////////////////////////////////////////////////////////////
/// Constructors
////////////////////////////////////////////////////////////////////////////////
inline uniform LinearSpace3f make_LinearSpace3f(const uniform Vec3f &x, const uniform Vec3f &y, const uniform Vec3f &z) {
uniform LinearSpace3f l; l.vx = x; l.vy = y; l.vz = z; return l;
}
inline varying LinearSpace3f make_LinearSpace3f(const varying Vec3f &x, const varying Vec3f &y, const varying Vec3f &z) {
varying LinearSpace3f l; l.vx = x; l.vy = y; l.vz = z; return l;
}
inline uniform LinearSpace3f make_LinearSpace3f(const uniform LinearSpace3fa &s) {
uniform LinearSpace3f l; l.vx = make_Vec3f(s.vx); l.vy = make_Vec3f(s.vy); l.vz = make_Vec3f(s.vz); return l;
}
inline varying LinearSpace3f make_LinearSpace3f(const varying LinearSpace3fa &s) {
varying LinearSpace3f l; l.vx = make_Vec3f(s.vx); l.vy = make_Vec3f(s.vy); l.vz = make_Vec3f(s.vz); return l;
}
/*! construction from quaternion */
inline uniform LinearSpace3f make_LinearSpace3f(const uniform Quaternion3f& q)
{
uniform LinearSpace3f l;
l.vx = make_Vec3f(q.r*q.r + q.i*q.i - q.j*q.j - q.k*q.k, 2.0f*(q.i*q.j + q.r*q.k), 2.0f*(q.i*q.k - q.r*q.j));
l.vy = make_Vec3f(2.0f*(q.i*q.j - q.r*q.k), (q.r*q.r - q.i*q.i + q.j*q.j - q.k*q.k), 2.0f*(q.j*q.k + q.r*q.i));
l.vz = make_Vec3f(2.0f*(q.i*q.k + q.r*q.j), 2.0f*(q.j*q.k - q.r*q.i), q.r*q.r - q.i*q.i - q.j*q.j + q.k*q.k);
return l;
}
inline varying LinearSpace3f make_LinearSpace3f(const varying Quaternion3f& q)
{
LinearSpace3f l;
l.vx = make_Vec3f(q.r*q.r + q.i*q.i - q.j*q.j - q.k*q.k, 2.0f*(q.i*q.j + q.r*q.k), 2.0f*(q.i*q.k - q.r*q.j));
l.vy = make_Vec3f(2.0f*(q.i*q.j - q.r*q.k), (q.r*q.r - q.i*q.i + q.j*q.j - q.k*q.k), 2.0f*(q.j*q.k + q.r*q.i));
l.vz = make_Vec3f(2.0f*(q.i*q.k + q.r*q.j), 2.0f*(q.j*q.k - q.r*q.i), q.r*q.r - q.i*q.i - q.j*q.j + q.k*q.k);
return l;
}
inline uniform LinearSpace3f make_LinearSpace3f_identity()
{
return make_LinearSpace3f(make_Vec3f(1.f,0.f,0.f),
make_Vec3f(0.f,1.f,0.f),
make_Vec3f(0.f,0.f,1.f));
}
/*! return scale matrix */
inline uniform LinearSpace3f make_LinearSpace3f_scale(const uniform Vec3f& s)
{
return make_LinearSpace3f( make_Vec3f( s.x, 0.0f, 0.0f),
make_Vec3f(0.0f, s.y, 0.0f),
make_Vec3f(0.0f, 0.0f, s.z));
}
/*! return matrix for rotation around arbitrary axis */
inline uniform LinearSpace3f make_LinearSpace3f_rotate(const uniform Vec3f& _u, const uniform float& r)
{
uniform Vec3f u = normalize(_u);
uniform float s = sin(r), c = cos(r);
return make_LinearSpace3f(make_Vec3f(u.x*u.x+(1-u.x*u.x)*c, u.x*u.y*(1-c)+u.z*s, u.x*u.z*(1-c)-u.y*s),
make_Vec3f(u.x*u.y*(1-c)-u.z*s, u.y*u.y+(1-u.y*u.y)*c, u.y*u.z*(1-c)+u.x*s),
make_Vec3f(u.x*u.z*(1-c)+u.y*s, u.y*u.z*(1-c)-u.x*s, u.z*u.z+(1-u.z*u.z)*c));
}
/*! return matrix for rotation around arbitrary axis */
inline varying LinearSpace3f make_LinearSpace3f_rotate(const varying Vec3f& _u, const varying float& r)
{
varying Vec3f u = normalize(_u);
varying float s = sin(r), c = cos(r);
return make_LinearSpace3f(make_Vec3f(u.x*u.x+(1-u.x*u.x)*c, u.x*u.y*(1-c)+u.z*s, u.x*u.z*(1-c)-u.y*s),
make_Vec3f(u.x*u.y*(1-c)-u.z*s, u.y*u.y+(1-u.y*u.y)*c, u.y*u.z*(1-c)+u.x*s),
make_Vec3f(u.x*u.z*(1-c)+u.y*s, u.y*u.z*(1-c)-u.x*s, u.z*u.z+(1-u.z*u.z)*c));
}
/*! return matrix for rotation around arbitrary axis */
inline varying LinearSpace3f make_LinearSpace3f_rotate(const uniform Vec3f& _u, const varying float& r)
{
varying Vec3f u = normalize(_u);
varying float s = sin(r), c = cos(r);
return make_LinearSpace3f(make_Vec3f(u.x*u.x+(1-u.x*u.x)*c, u.x*u.y*(1-c)+u.z*s, u.x*u.z*(1-c)-u.y*s),
make_Vec3f(u.x*u.y*(1-c)-u.z*s, u.y*u.y+(1-u.y*u.y)*c, u.y*u.z*(1-c)+u.x*s),
make_Vec3f(u.x*u.z*(1-c)+u.y*s, u.y*u.z*(1-c)-u.x*s, u.z*u.z+(1-u.z*u.z)*c));
}
////////////////////////////////////////////////////////////////////////////////
// Unary Operators
////////////////////////////////////////////////////////////////////////////////
inline uniform LinearSpace3f neg(const uniform LinearSpace3f &l) { return make_LinearSpace3f(neg(l.vx),neg(l.vy),neg(l.vz)); }
inline varying LinearSpace3f neg(const varying LinearSpace3f &l) { return make_LinearSpace3f(neg(l.vx),neg(l.vy),neg(l.vz)); }
/*! compute the determinant of the matrix */
inline uniform float det(const uniform LinearSpace3f &l) { return dot(l.vx,cross(l.vy,l.vz)); }
inline varying float det(const varying LinearSpace3f &l) { return dot(l.vx,cross(l.vy,l.vz)); }
/*! compute transposed matrix */
inline uniform LinearSpace3f transposed(const uniform LinearSpace3f &l) {
return make_LinearSpace3f(make_Vec3f(l.vx.x,l.vy.x,l.vz.x),
make_Vec3f(l.vx.y,l.vy.y,l.vz.y),
make_Vec3f(l.vx.z,l.vy.z,l.vz.z));
}
inline varying LinearSpace3f transposed(const varying LinearSpace3f &l) {
return make_LinearSpace3f(make_Vec3f(l.vx.x,l.vy.x,l.vz.x),
make_Vec3f(l.vx.y,l.vy.y,l.vz.y),
make_Vec3f(l.vx.z,l.vy.z,l.vz.z));
}
/*! compute adjoint matrix */
inline uniform LinearSpace3f adjoint(const uniform LinearSpace3f &l) {
return transposed(make_LinearSpace3f(cross(l.vy,l.vz),cross(l.vz,l.vx),cross(l.vx,l.vy)));
}
inline varying LinearSpace3f adjoint(const varying LinearSpace3f &l) {
return transposed(make_LinearSpace3f(cross(l.vy,l.vz),cross(l.vz,l.vx),cross(l.vx,l.vy)));
}
/*! calculates orthogonal coordinate frame with z-Vector pointing towards N */
inline uniform LinearSpace3f frame(const uniform Vec3f &N)
{
const uniform Vec3f dx0 = make_Vec3f(0.0f,N.z,-N.y);
const uniform Vec3f dx1 = make_Vec3f(-N.z,0.0f,N.x);
const uniform Vec3f dx = normalize(dot(dx0,dx0) > dot(dx1,dx1) ? dx0 : dx1);
const uniform Vec3f dy = normalize(cross(N,dx));
return make_LinearSpace3f(dx,dy,N);
}
inline varying LinearSpace3f frame(const varying Vec3f &N)
{
const varying Vec3f dx0 = make_Vec3f(0.0f,N.z,-N.y);
const varying Vec3f dx1 = make_Vec3f(-N.z,0.0f,N.x);
const varying Vec3f dx = normalize(dot(dx0,dx0) > dot(dx1,dx1) ? dx0 : dx1);
const varying Vec3f dy = normalize(cross(N,dx));
return make_LinearSpace3f(dx,dy,N);
}
////////////////////////////////////////////////////////////////////////////////
/// Binary Operators
////////////////////////////////////////////////////////////////////////////////
inline uniform LinearSpace3f operator+(const uniform LinearSpace3f &a, const uniform LinearSpace3f &b) { return make_LinearSpace3f(a.vx+b.vx, a.vy+b.vy, a.vz+b.vz); }
inline varying LinearSpace3f operator+(const varying LinearSpace3f &a, const varying LinearSpace3f &b) { return make_LinearSpace3f(a.vx+b.vx, a.vy+b.vy, a.vz+b.vz); }
inline uniform LinearSpace3f operator-(const uniform LinearSpace3f &a, const uniform LinearSpace3f &b) { return make_LinearSpace3f(a.vx-b.vx, a.vy-b.vy, a.vz-b.vz); }
inline varying LinearSpace3f operator-(const varying LinearSpace3f &a, const varying LinearSpace3f &b) { return make_LinearSpace3f(a.vx-b.vx, a.vy-b.vy, a.vz-b.vz); }
inline uniform Vec3f operator*(const uniform LinearSpace3f &l, const uniform Vec3f &v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
inline varying Vec3f operator*(const uniform LinearSpace3f &l, const varying Vec3f &v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
inline varying Vec3f operator*(const varying LinearSpace3f &l, const varying Vec3f &v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
inline uniform LinearSpace3f operator*(const uniform float &a, const uniform LinearSpace3f &b) { return make_LinearSpace3f(a*b.vx, a*b.vy, a*b.vz); }
inline uniform LinearSpace3f operator*(const uniform LinearSpace3f &a, const uniform float &b) { return make_LinearSpace3f(a.vx*b, a.vy*b, a.vz*b); }
inline uniform LinearSpace3f operator*(const uniform LinearSpace3f &a, const uniform LinearSpace3f &b) { return make_LinearSpace3f(a*b.vx, a*b.vy, a*b.vz); }
inline varying LinearSpace3f operator*(const varying float &a, const varying LinearSpace3f &b) { return make_LinearSpace3f(a*b.vx, a*b.vy, a*b.vz); }
inline varying LinearSpace3f operator*(const varying LinearSpace3f &a, const varying float &b) { return make_LinearSpace3f(a.vx*b, a.vy*b, a.vz*b); }
inline varying LinearSpace3f operator*(const varying LinearSpace3f &a, const varying LinearSpace3f &b) { return make_LinearSpace3f(a*b.vx, a*b.vy, a*b.vz); }
inline varying LinearSpace3f operator*(const varying float &a, const uniform LinearSpace3f &b) { return make_LinearSpace3f(a*b.vx, a*b.vy, a*b.vz); }
inline varying LinearSpace3f operator*(const uniform LinearSpace3f &a, const varying float &b) { return make_LinearSpace3f(a.vx*b, a.vy*b, a.vz*b); }
inline uniform Vec3f xfmVector(const uniform LinearSpace3f l, const uniform Vec3f v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
inline varying Vec3f xfmVector(const uniform LinearSpace3f l, const varying Vec3f v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
inline varying Vec3f xfmVector(const varying LinearSpace3f l, const varying Vec3f v) { return v.x*l.vx + v.y*l.vy + v.z*l.vz; }
////////////////////////////////////////////////////////////////////////////////
/// Comparison Operators
////////////////////////////////////////////////////////////////////////////////
inline uniform bool eq(const uniform LinearSpace3f &a, const uniform LinearSpace3f &b) { return eq(a.vx,b.vx) & eq(a.vy,b.vy) & eq(a.vz,b.vz); }
inline varying bool eq(const varying LinearSpace3f &a, const varying LinearSpace3f &b) { return eq(a.vx,b.vx) & eq(a.vy,b.vy) & eq(a.vz,b.vz); }
inline uniform bool ne(const uniform LinearSpace3f &a, const uniform LinearSpace3f &b) { return ne(a.vx,b.vx) | ne(a.vy,b.vy) | ne(a.vz,b.vz); }
inline varying bool ne(const varying LinearSpace3f &a, const varying LinearSpace3f &b) { return ne(a.vx,b.vx) | ne(a.vy,b.vy) | ne(a.vz,b.vz); }
////////////////////////////////////////////////////////////////////////////////
// Unary Operators
////////////////////////////////////////////////////////////////////////////////
/*! compute inverse matrix */
inline uniform LinearSpace3f rcp(const uniform LinearSpace3f &l) { return rcp(det(l))*adjoint(l); }
inline varying LinearSpace3f rcp(const varying LinearSpace3f &l) { return rcp(det(l))*adjoint(l); }
inline uniform Vec3f xfmNormal(const uniform LinearSpace3f l, const uniform Vec3f v) { return xfmVector(transposed(rcp(l)),v); }
inline varying Vec3f xfmNormal(const uniform LinearSpace3f l, const varying Vec3f v) { return xfmVector(transposed(rcp(l)),v); }
inline varying Vec3f xfmNormal(const varying LinearSpace3f l, const varying Vec3f v) { return xfmVector(transposed(rcp(l)),v); }
////////////////////////////////////////////////////////////////////////////////
// Interpolation
////////////////////////////////////////////////////////////////////////////////
inline uniform LinearSpace3f lerp(uniform float factor, const uniform LinearSpace3f& a, const uniform LinearSpace3f& b) {
return make_LinearSpace3f(lerp(factor, a.vx, b.vx), lerp(factor, a.vy, b.vy), lerp(factor, a.vz, b.vz));
}
inline varying LinearSpace3f lerp(varying float factor, const uniform LinearSpace3f& a, const uniform LinearSpace3f& b) {
return make_LinearSpace3f(lerp(factor, a.vx, b.vx), lerp(factor, a.vy, b.vy), lerp(factor, a.vz, b.vz));
}
inline varying LinearSpace3f lerp(varying float factor, const varying LinearSpace3f& a, const varying LinearSpace3f& b) {
return make_LinearSpace3f(lerp(factor, a.vx, b.vx), lerp(factor, a.vy, b.vy), lerp(factor, a.vz, b.vz));
}
////////////////////////////////////////////////////////////////////////////////
// Norms
////////////////////////////////////////////////////////////////////////////////
inline uniform float norm_1(const uniform LinearSpace3f& l)
{
uniform float sum = 0;
sum += reduce_add(abs(l.vx));
sum += reduce_add(abs(l.vy));
sum += reduce_add(abs(l.vz));
return sum / 9.f;
}
inline uniform Quaternion3f make_Quaternion3f(const uniform LinearSpace3f & l)
{
uniform Quaternion3f q;
const uniform float tr = l.vx.x + l.vy.y + l.vz.z;
if (tr > 0)
{
const uniform float S = sqrt(tr+1.0) * 2;
q.r = 0.25 * S;
q.i = (l.vy.z - l.vz.y) / S;
q.j = (l.vz.x - l.vx.z) / S;
q.k = (l.vx.y - l.vy.x) / S;
}
else if ((l.vx.x > l.vy.y)&(l.vx.x > l.vz.z))
{
const uniform float S = sqrt(1.0 + l.vx.x - l.vy.y - l.vz.z) * 2;
q.r = (l.vy.z - l.vz.y) / S;
q.i = 0.25 * S;
q.j = (l.vy.x + l.vx.y) / S;
q.k = (l.vz.x + l.vx.z) / S;
}
else if (l.vy.y > l.vz.z)
{
const uniform float S = sqrt(1.0 + l.vy.y - l.vx.x - l.vz.z) * 2;
q.r = (l.vz.x - l.vx.z) / S;
q.i = (l.vy.x + l.vx.y) / S;
q.j = 0.25 * S;
q.k = (l.vz.y + l.vy.z) / S;
}
else
{
const uniform float S = sqrt(1.0 + l.vz.z - l.vx.x - l.vy.y) * 2;
q.r = (l.vx.y - l.vy.x) / S;
q.i = (l.vz.x + l.vx.z) / S;
q.j = (l.vz.y + l.vy.z) / S;
q.k = 0.25 * S;
}
return q;
}
inline varying Quaternion3f make_Quaternion3f(const varying LinearSpace3f & l)
{
Quaternion3f q;
const float tr = l.vx.x + l.vy.y + l.vz.z;
if (tr > 0)
{
const float S = sqrt(tr+1.0) * 2;
q.r = 0.25 * S;
q.i = (l.vy.z - l.vz.y) / S;
q.j = (l.vz.x - l.vx.z) / S;
q.k = (l.vx.y - l.vy.x) / S;
}
else if ((l.vx.x > l.vy.y)&(l.vx.x > l.vz.z))
{
const float S = sqrt(1.0 + l.vx.x - l.vy.y - l.vz.z) * 2;
q.r = (l.vy.z - l.vz.y) / S;
q.i = 0.25 * S;
q.j = (l.vy.x + l.vx.y) / S;
q.k = (l.vz.x + l.vx.z) / S;
}
else if (l.vy.y > l.vz.z)
{
const float S = sqrt(1.0 + l.vy.y - l.vx.x - l.vz.z) * 2;
q.r = (l.vz.x - l.vx.z) / S;
q.i = (l.vy.x + l.vx.y) / S;
q.j = 0.25 * S;
q.k = (l.vz.y + l.vy.z) / S;
}
else
{
const float S = sqrt(1.0 + l.vz.z - l.vx.x - l.vy.y) * 2;
q.r = (l.vx.y - l.vy.x) / S;
q.i = (l.vz.x + l.vx.z) / S;
q.j = (l.vz.y + l.vy.z) / S;
q.k = 0.25 * S;
}
return q;
}