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