369 lines
9.3 KiB
C++
369 lines
9.3 KiB
C++
/* -*- C++ -*- ------------------------------------------------------------
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Copyright (c) 2007 Jesse Anders and Demian Nave http://cmldev.net/
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The Configurable Math Library (CML) is distributed under the terms of the
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Boost Software License, v1.0 (see cml/LICENSE for details).
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*-----------------------------------------------------------------------*/
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/** @file
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* @brief
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*/
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#ifndef cml_util_h
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#define cml_util_h
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#include <algorithm> // For std::min and std::max.
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#include <cstdlib> // For std::rand.
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#include <cml/constants.h>
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#if defined(_MSC_VER)
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#pragma push_macro("min")
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#pragma push_macro("max")
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#undef min
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#undef max
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#endif
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namespace cml {
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/** Sign of input value as double. */
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template < typename T >
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double sign(T value) {
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return value < T(0) ? -1.0 : (value > T(0) ? 1.0 : 0.0);
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}
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/** Clamp input value to the range [min, max]. */
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template < typename T >
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T clamp(T value, T min, T max) {
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return std::max(std::min(value, max), min);
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}
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/** Test input value for inclusion in [min, max]. */
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template < typename T >
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bool in_range(T value, T min, T max) {
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return !(value < min) && !(value > max);
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}
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/** Map input value from [min1, max1] to [min2, max2]. */
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template < typename T >
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T map_range(T value, T min1, T max1, T min2, T max2) {
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return min2 + ((value - min1) / (max1 - min1)) * (max2 - min2);
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}
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/** Wrap std::acos() and clamp argument to [-1, 1]. */
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template < typename T >
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T acos_safe(T theta) {
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return T(std::acos(clamp(theta, T(-1.0), T(1.0))));
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}
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/** Wrap std::asin() and clamp argument to [-1, 1]. */
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template < typename T >
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T asin_safe(T theta) {
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return T(std::asin(clamp(theta, T(-1.0), T(1.0))));
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}
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/** Wrap std::sqrt() and clamp argument to [0, inf). */
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template < typename T >
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T sqrt_safe(T value) {
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return T(std::sqrt(std::max(value, T(0.0))));
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}
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/** Square a value. */
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template < typename T >
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T sqr(T value) {
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return value * value;
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}
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/** Cube a value. */
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template < typename T >
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T cub(T value) {
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return value * value * value;
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}
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/** Inverse square root. */
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template < typename T >
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T inv_sqrt(T value) {
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return T(1.0 / std::sqrt(value));
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}
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/* The next few functions deal with indexing. next() and prev() are useful
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* for operations involving the vertices of a polygon or other cyclic set,
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* and cyclic_permutation() is used by various functions that deal with
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* axes or basis vectors in a generic way. As these functions are only
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* relevant for unsigned integer types, I've just used size_t, but there
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* may be reasons I haven't thought of that they should be templated.
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*/
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/** Return next, with cycling, in a series of N non-negative integers. */
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inline size_t next(size_t i, size_t N) {
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return (i + 1) % N;
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}
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/** Return previous, with cycling, in a series of N non-negative integers. */
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inline size_t prev(size_t i, size_t N) {
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return i ? (i - 1) : (N - 1);
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}
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/** Cyclic permutation of the set { 0, 1 }, starting with 'first'. */
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inline void cyclic_permutation(size_t first, size_t& i, size_t& j) {
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i = first;
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j = next(i, 2);
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}
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/** Cyclic permutation of the set { 0, 1, 2 }, starting with 'first'. */
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inline void cyclic_permutation(size_t first, size_t& i, size_t& j, size_t& k)
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{
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i = first;
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j = next(i, 3);
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k = next(j, 3);
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}
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/** Cyclic permutation of the set { 0, 1, 2, 3 }, starting with 'first'. */
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inline void cyclic_permutation(
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size_t first, size_t& i, size_t& j, size_t& k, size_t& l)
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{
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i = first;
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j = next(i, 4);
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k = next(j, 4);
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l = next(k, 4);
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}
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/** Convert radians to degrees. */
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template < typename T >
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T deg(T theta) {
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return theta * constants<T>::deg_per_rad();
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}
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/** Convert degrees to radians. */
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template < typename T >
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T rad(T theta) {
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return theta * constants<T>::rad_per_deg();
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}
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/* Note: Moving interpolation functions to interpolation.h */
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#if 0
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/** Linear interpolation of 2 values.
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*
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* @note The data points are assumed to be sampled at u = 0 and u = 1, so
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* for interpolation u must lie between 0 and 1.
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*/
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template <typename T, typename Scalar>
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T lerp(const T& f0, const T& f1, Scalar u) {
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return (Scalar(1.0) - u) * f0 + u * f1;
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}
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#endif
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#if 0
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/** Bilinear interpolation of 4 values.
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*
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* @note The data points are assumed to be sampled at the corners of a unit
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* square, so for interpolation u and v must lie between 0 and 1,
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*/
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template <typename T, typename Scalar>
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T bilerp(const T& f00, const T& f10,
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const T& f01, const T& f11,
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Scalar u, Scalar v)
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{
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Scalar uv = u * v;
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return (
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(Scalar(1.0) - u - v + uv) * f00 +
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(u - uv) * f10 +
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(v - uv) * f01 +
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uv * f11
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);
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}
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#endif
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#if 0
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/** Trilinear interpolation of 8 values.
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*
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* @note The data values are assumed to be sampled at the corners of a unit
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* cube, so for interpolation, u, v, and w must lie between 0 and 1.
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*/
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template <typename T, typename Scalar>
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T trilerp(const T& f000, const T& f100,
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const T& f010, const T& f110,
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const T& f001, const T& f101,
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const T& f011, const T& f111,
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Scalar u, Scalar v, Scalar w)
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{
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Scalar uv = u * v;
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Scalar vw = v * w;
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Scalar wu = w * u;
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Scalar uvw = uv * w;
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return (
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(Scalar(1.0) - u - v - w + uv + vw + wu - uvw) * f000 +
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(u - uv - wu + uvw) * f100 +
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(v - uv - vw + uvw) * f010 +
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(uv - uvw) * f110 +
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(w - vw - wu + uvw) * f001 +
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(wu - uvw) * f101 +
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(vw - uvw) * f011 +
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uvw * f111
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);
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}
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#endif
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/** Random binary (0,1) value. */
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inline size_t random_binary() {
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return std::rand() % 2;
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}
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/** Random polar (-1,1) value. */
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inline int random_polar() {
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return random_binary() ? 1 : -1;
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}
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/** Random real in [0,1]. */
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inline double random_unit() {
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return double(std::rand()) / double(RAND_MAX);
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}
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/* Random integer in the range [min, max] */
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inline long random_integer(long min, long max) {
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return min + std::rand() % (max - min + 1);
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}
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/* Random real number in the range [min, max] */
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template < typename T >
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T random_real(T min, T max) {
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return min + static_cast<T>(random_unit()) * (max - min);
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}
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/** Squared length in R2. */
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template < typename T >
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T length_squared(T x, T y) {
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return x * x + y * y;
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}
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/** Squared length in R3. */
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template < typename T >
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T length_squared(T x, T y, T z) {
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return x * x + y * y + z * z;
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}
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/** Length in R2. */
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template < typename T >
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T length(T x, T y) {
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return std::sqrt(length_squared(x,y));
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}
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/** Length in R3. */
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template < typename T >
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T length(T x, T y, T z) {
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return std::sqrt(length_squared(x,y,z));
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}
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/** Index of maximum of 2 values. */
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template < typename T >
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size_t index_of_max(T a, T b) {
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return a > b ? 0 : 1;
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}
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/** Index of maximum of 2 values by magnitude. */
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template < typename T >
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size_t index_of_max_abs(T a, T b) {
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return index_of_max(std::fabs(a),std::fabs(b));
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}
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/** Index of minimum of 2 values. */
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template < typename T >
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size_t index_of_min(T a, T b) {
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return a < b ? 0 : 1;
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}
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/** Index of minimum of 2 values by magnitude. */
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template < typename T >
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size_t index_of_min_abs(T a, T b) {
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return index_of_min(std::fabs(a),std::fabs(b));
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}
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/** Index of maximum of 3 values. */
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template < typename T >
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size_t index_of_max(T a, T b, T c) {
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return a > b ? (c > a ? 2 : 0) : (b > c ? 1 : 2);
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}
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/** Index of maximum of 3 values by magnitude. */
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template < typename T >
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size_t index_of_max_abs(T a, T b, T c) {
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return index_of_max(std::fabs(a),std::fabs(b),std::fabs(c));
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}
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/** Index of minimum of 3 values. */
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template < typename T >
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size_t index_of_min(T a, T b, T c) {
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return a < b ? (c < a ? 2 : 0) : (b < c ? 1 : 2);
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}
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/** Index of minimum of 3 values by magnitude. */
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template < typename T >
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size_t index_of_min_abs(T a, T b, T c) {
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return index_of_min(std::fabs(a),std::fabs(b),std::fabs(c));
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}
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/** Wrap input value to the range [min,max]. */
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template < typename T >
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T wrap(T value, T min, T max) {
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max -= min;
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value = std::fmod(value - min, max);
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if (value < T(0)) {
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value += max;
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}
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return min + value;
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}
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/** Convert horizontal field of view to vertical field of view. */
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template < typename T >
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T xfov_to_yfov(T xfov, T aspect) {
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return T(2.0 * std::atan(std::tan(xfov * T(.5)) / double(aspect)));
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}
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/** Convert vertical field of view to horizontal field of view. */
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template < typename T >
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T yfov_to_xfov(T yfov, T aspect) {
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return T(2.0 * std::atan(std::tan(yfov * T(.5)) * double(aspect)));
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}
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/** Convert horizontal zoom to vertical zoom. */
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template < typename T >
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T xzoom_to_yzoom(T xzoom, T aspect) {
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return xzoom * aspect;
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}
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/** Convert vertical zoom to horizontal zoom. */
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template < typename T >
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T yzoom_to_xzoom(T yzoom, T aspect) {
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return yzoom / aspect;
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}
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/** Convert zoom factor to field of view. */
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template < typename T >
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T zoom_to_fov(T zoom) {
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return T(2) * T(std::atan(T(1) / zoom));
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}
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/** Convert field of view to zoom factor. */
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template < typename T >
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T fov_to_zoom(T fov) {
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return T(1) / T(std::tan(fov * T(.5)));
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}
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} // namespace cml
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#if defined(_MSC_VER)
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#pragma pop_macro("min")
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#pragma pop_macro("max")
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#endif
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#endif
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// -------------------------------------------------------------------------
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// vim:ft=cpp
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