Commit 1b7ab224 authored by Lázár Bence Kis's avatar Lázár Bence Kis
Browse files

Newton-Raphson uses the previous result as its initial guess

parent 7096d0dc

anim/include/anim/interpolator.hpp

+8 −5
Original line number Diff line number Diff line
@@ -27,7 +27,7 @@ std::vector<scalar> cardanoSolve(scalar a, scalar b, scalar c, scalar d); 
vec2   evaluateBezierDerivative(const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar t);

vec2   evaluateBezier          (const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar t);

scalar solveBezierCardano      (const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar targetX);

scalar solveBezierNewtonRaphson(const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar targetX);

scalar solveBezierNewtonRaphson(const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar targetX, scalar initialGuess);



} // namespace helpers
@@ -128,14 +128,16 @@ struct BezierInterpolator : public Interpolator<T> { 
        scalar t = p0.x + normalizedTime * (p3.x - p0.x);



        if constexpr (Method == NEWTON_RAPHSON) {

            return helpers::solveBezierNewtonRaphson(p0, p1, p2, p3, t);

            m_tSolved = helpers::solveBezierNewtonRaphson(p0, p1, p2, p3, t, m_tSolved);

        }

        else if constexpr (Method == CARDANO) {

            return helpers::solveBezierCardano(p0, p1, p2, p3, t);

            m_tSolved = helpers::solveBezierCardano(p0, p1, p2, p3, t);

        }

        else {

            throw std::runtime_error("Unknown Bezier method!");

        }



        return helpers::evaluateBezier(p0, p1, p2, p3, m_tSolved).y;

    }

    

    T interpolate(const Keyframe<T>& start, const Keyframe<T>& end, scalar normalizedTime) const override
@@ -171,8 +173,8 @@ struct BezierInterpolator : public Interpolator<T> { 
    std::array<vec2, 2> getControlPoints(const Keyframe<T>& start, const Keyframe<T>& end) const

    {

        return {

            vec2{ start.time() + m_handles.leftHandle.x, start.value/* <scalar> */() + m_handles.leftHandle.y },

            vec2{ end.time() + m_handles.rightHandle.x, end.value/* <scalar> */() + m_handles.rightHandle.y }

            vec2{ start.time() + m_handles.leftHandle.x, start.value() + m_handles.leftHandle.y },

            vec2{ end.time() + m_handles.rightHandle.x, end.value() + m_handles.rightHandle.y }

        };

    }
@@ -183,6 +185,7 @@ struct BezierInterpolator : public Interpolator<T> { 


private:

    BezierHandles m_handles;

    mutable scalar m_tSolved = 0.5_s;

};



// Concrete interpolator for ease in/out

anim/src/interpolator.cpp

+4 −6
Original line number Diff line number Diff line
@@ -95,13 +95,13 @@ scalar solveBezierCardano( 
        }

    }



    return static_cast<scalar>(evaluateBezier(p0, p1, p2, p3, tSolved).y);

    return tSolved;

}



scalar solveBezierNewtonRaphson(const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar targetX) {

scalar solveBezierNewtonRaphson(const vec2& p0, const vec2& p1, const vec2& p2, const vec2& p3, scalar targetX, scalar initialGuess) {

    // Newton-Raphson iteration to find the t value for desired x

    const int MAX_ITERATIONS = 8;

    scalar currentT = 0.5_s;

    scalar currentT = initialGuess;

    

    for (int i = 0; i < MAX_ITERATIONS; i++) {

        vec2 point = evaluateBezier(p0, p1, p2, p3, currentT);
@@ -118,9 +118,7 @@ scalar solveBezierNewtonRaphson(const vec2& p0, const vec2& p1, const vec2& p2, 
        currentT = currentT - f / df;

        currentT = clamp(currentT, 0.0_s, 1.0_s);

    }

    

    vec2 finalPoint = evaluateBezier(p0, p1, p2, p3, currentT);

    return finalPoint.y;

    return currentT;

}



} // namespace helpers