mathUtils.h

//
// Copyright 2023 Pixar
//
// Licensed under the terms set forth in the LICENSE.txt file available at
// https://openusd.org/license.
//
 
#ifndef PXR_BASE_TS_MATH_UTILS_H
#define PXR_BASE_TS_MATH_UTILS_H
 
#include "pxr/pxr.h"
#include "pxr/base/ts/api.h"
#include "pxr/base/ts/types.h"
 
PXR_NAMESPACE_OPEN_SCOPE
 
class GfMatrix4d;
 
// Solve the cubic polynomial time=f(u) where
// f(u) = c[0] + u * c[1] + u^2 * c[2] + u^3 * c[3].
// XXX: exported because used by templated functions starting from TsEvaluator
TS_API
double Ts_SolveCubic(const TsTime c[4], TsTime time);
 
// Take the first derivative of a cubic polynomial:
//   3*c[3]*u^2 + 2*c[2] + c[1]
template <typename T>
void
Ts_CubicDerivative( const T poly[4], double deriv[3] )
{
    deriv[2] = 3. * poly[3];
    deriv[1] = 2. * poly[2];
    deriv[0] =      poly[1];
}
 
// Solve f(x) = y for x in the given bounds where f is a cubic polynomial.
double
Ts_SolveCubicInInterval(
    const TsTime poly[4], const TsTime polyDeriv[3],
    TsTime y, const GfInterval& bounds);
 
// Solve for the roots of a quadratic equation.
bool
Ts_SolveQuadratic( const double poly[3], double *root0, double *root1 );
 
// Evaluate the quadratic polynomial in c[] at u.
template <typename T>
T
Ts_EvalQuadratic(const T c[3], double u)
{
    return u * (u * c[2] + c[1]) + c[0];
}
 
// Evaluate the cubic polynomial in c[] at u.
template <typename T>
T
Ts_EvalCubic(const T c[4], double u)
{
    return u * (u * (u * c[3] + c[2]) + c[1]) + c[0];
}
 
template <typename T>
T
Ts_EvalCubicDerivative(const T c[4], double u)
{
    return u * (u * 3.0 * c[3] + 2.0 * c[2]) + c[1];
}
 
PXR_NAMESPACE_CLOSE_SCOPE
 
#endif