Spline.cpp

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/*
* This file is part of Project SkyFire https://www.projectskyfire.org.
* See LICENSE.md file for Copyright information
*/
 
#include "Spline.h"
#include <G3D/Matrix4.h>
#include <sstream>
 
namespace Movement
{
    SplineBase::EvaluationMethtod SplineBase::evaluators[SplineBase::ModesEnd] =
    {
        &SplineBase::EvaluateLinear,
        &SplineBase::EvaluateCatmullRom,
        &SplineBase::EvaluateBezier3,
        (EvaluationMethtod)&SplineBase::UninitializedSpline,
    };
 
    SplineBase::EvaluationMethtod SplineBase::derivative_evaluators[SplineBase::ModesEnd] =
    {
        &SplineBase::EvaluateDerivativeLinear,
        &SplineBase::EvaluateDerivativeCatmullRom,
        &SplineBase::EvaluateDerivativeBezier3,
        (EvaluationMethtod)&SplineBase::UninitializedSpline,
    };
 
    SplineBase::SegLenghtMethtod SplineBase::seglengths[SplineBase::ModesEnd] =
    {
        &SplineBase::SegLengthLinear,
        &SplineBase::SegLengthCatmullRom,
        &SplineBase::SegLengthBezier3,
        (SegLenghtMethtod)&SplineBase::UninitializedSpline,
    };
 
    SplineBase::InitMethtod SplineBase::initializers[SplineBase::ModesEnd] =
    {
        //&SplineBase::InitLinear,
        &SplineBase::InitCatmullRom,    // we should use catmullrom initializer even for linear mode! (client's internal structure limitation)
        &SplineBase::InitCatmullRom,
        &SplineBase::InitBezier3,
        (InitMethtod)&SplineBase::UninitializedSpline,
    };

 
    using G3D::Matrix4;
    static const Matrix4 s_catmullRomCoeffs(
        -0.5f, 1.5f, -1.5f, 0.5f,
        1.f, -2.5f, 2.f, -0.5f,
        -0.5f, 0.f, 0.5f, 0.f,
        0.f, 1.f, 0.f, 0.f);
 
    static const Matrix4 s_Bezier3Coeffs(
        -1.f, 3.f, -3.f, 1.f,
        3.f, -6.f, 3.f, 0.f,
        -3.f, 3.f, 0.f, 0.f,
        1.f, 0.f, 0.f, 0.f);
 
    /*  classic view:
    inline void C_Evaluate(const Vector3 *vertice, float t, const float (&matrix)[4][4], Vector3 &position)
    {
        Vector3 tvec(t*t*t, t*t, t);
        int i = 0;
        double c;
        double x = 0, y = 0, z = 0;
        while ( i < 4 )
        {
            c = matrix[0][i]*tvec.x + matrix[1][i]*tvec.y + matrix[2][i]*tvec.z + matrix[3][i];
 
            x += c * vertice->x;
            y += c * vertice->y;
            z += c * vertice->z;
 
            ++i;
            ++vertice;
        }
 
        position.x = x;
        position.y = y;
        position.z = z;
    }*/
 
    inline void C_Evaluate(const Vector3* vertice, float t, const Matrix4& matr, Vector3& result)
    {
        Vector4 tvec(t * t * t, t * t, t, 1.f);
        Vector4 weights(tvec * matr);
 
        result = vertice[0] * weights[0] + vertice[1] * weights[1]
            + vertice[2] * weights[2] + vertice[3] * weights[3];
    }
 
    inline void C_Evaluate_Derivative(const Vector3* vertice, float t, const Matrix4& matr, Vector3& result)
    {
        Vector4 tvec(3.f * t * t, 2.f * t, 1.f, 0.f);
        Vector4 weights(tvec * matr);
 
        result = vertice[0] * weights[0] + vertice[1] * weights[1]
            + vertice[2] * weights[2] + vertice[3] * weights[3];
    }
 
    void SplineBase::EvaluateLinear(index_type index, float u, Vector3& result) const
    {
        ASSERT(index >= index_lo && index < index_hi);
        result = points[index] + (points[index + 1] - points[index]) * u;
    }
 
    void SplineBase::EvaluateCatmullRom(index_type index, float t, Vector3& result) const
    {
        ASSERT(index >= index_lo && index < index_hi);
        C_Evaluate(&points[index - 1], t, s_catmullRomCoeffs, result);
    }
 
    void SplineBase::EvaluateBezier3(index_type index, float t, Vector3& result) const
    {
        index *= 3u;
        ASSERT(index >= index_lo && index < index_hi);
        C_Evaluate(&points[index], t, s_Bezier3Coeffs, result);
    }
 
    void SplineBase::EvaluateDerivativeLinear(index_type index, float, Vector3& result) const
    {
        ASSERT(index >= index_lo && index < index_hi);
        result = points[index + 1] - points[index];
    }
 
    void SplineBase::EvaluateDerivativeCatmullRom(index_type index, float t, Vector3& result) const
    {
        ASSERT(index >= index_lo && index < index_hi);
        C_Evaluate_Derivative(&points[index - 1], t, s_catmullRomCoeffs, result);
    }
 
    void SplineBase::EvaluateDerivativeBezier3(index_type index, float t, Vector3& result) const
    {
        index *= 3u;
        ASSERT(index >= index_lo && index < index_hi);
        C_Evaluate_Derivative(&points[index], t, s_Bezier3Coeffs, result);
    }
 
    float SplineBase::SegLengthLinear(index_type index) const
    {
        ASSERT(index >= index_lo && index < index_hi);
        return (points[index] - points[index + 1]).length();
    }
 
    float SplineBase::SegLengthCatmullRom(index_type index) const
    {
        ASSERT(index >= index_lo && index < index_hi);
 
        Vector3 curPos, nextPos;
        const Vector3* p = &points[index - 1];
        curPos = nextPos = p[1];
 
        index_type i = 1;
        double length = 0;
        while (i <= STEPS_PER_SEGMENT)
        {
            C_Evaluate(p, float(i) / float(STEPS_PER_SEGMENT), s_catmullRomCoeffs, nextPos);
            length += (nextPos - curPos).length();
            curPos = nextPos;
            ++i;
        }
        return length;
    }
 
    float SplineBase::SegLengthBezier3(index_type index) const
    {
        index *= 3u;
        ASSERT(index >= index_lo && index < index_hi);
 
        Vector3 curPos, nextPos;
        const Vector3* p = &points[index];
 
        C_Evaluate(p, 0.f, s_Bezier3Coeffs, nextPos);
        curPos = nextPos;
 
        index_type i = 1;
        double length = 0;
        while (i <= STEPS_PER_SEGMENT)
        {
            C_Evaluate(p, float(i) / float(STEPS_PER_SEGMENT), s_Bezier3Coeffs, nextPos);
            length += (nextPos - curPos).length();
            curPos = nextPos;
            ++i;
        }
        return length;
    }
 
    void SplineBase::init_spline(const Vector3* controls, index_type count, EvaluationMode m)
    {
        m_mode = m;
        cyclic = false;
 
        (this->*initializers[m_mode])(controls, count, cyclic, 0);
    }
 
    void SplineBase::init_cyclic_spline(const Vector3* controls, index_type count, EvaluationMode m, index_type cyclic_point)
    {
        m_mode = m;
        cyclic = true;
 
        (this->*initializers[m_mode])(controls, count, cyclic, cyclic_point);
    }
 
    void SplineBase::InitLinear(const Vector3* controls, index_type count, bool cyclic, index_type cyclic_point)
    {
        ASSERT(count >= 2);
        const int real_size = count + 1;
 
        points.resize(real_size);
 
        memcpy(&points[0], controls, sizeof(Vector3) * count);
 
        // first and last two indexes are space for special 'virtual points'
        // these points are required for proper C_Evaluate and C_Evaluate_Derivative methtod work
        if (cyclic)
            points[count] = controls[cyclic_point];
        else
            points[count] = controls[count - 1];
 
        index_lo = 0;
        index_hi = cyclic ? count : (count - 1);
    }
 
    void SplineBase::InitCatmullRom(const Vector3* controls, index_type count, bool cyclic, index_type cyclic_point)
    {
        const int real_size = count + (cyclic ? (1 + 2) : (1 + 1));
 
        points.resize(real_size);
 
        int lo_index = 1;
        int high_index = lo_index + count - 1;
 
        memcpy(&points[lo_index], controls, sizeof(Vector3) * count);
 
        // first and last two indexes are space for special 'virtual points'
        // these points are required for proper C_Evaluate and C_Evaluate_Derivative methtod work
        if (cyclic)
        {
            if (cyclic_point == 0)
                points[0] = controls[count - 1];
            else
                points[0] = controls[0].lerp(controls[1], -1);
 
            points[high_index + 1] = controls[cyclic_point];
            points[high_index + 2] = controls[cyclic_point + 1];
        }
        else
        {
            points[0] = controls[0].lerp(controls[1], -1);
            points[high_index + 1] = controls[count - 1];
        }
 
        index_lo = lo_index;
        index_hi = high_index + (cyclic ? 1 : 0);
    }
 
    void SplineBase::InitBezier3(const Vector3* controls, index_type count, bool /*cyclic*/, index_type /*cyclic_point*/)
    {
        index_type c = count / 3u * 3u;
        index_type t = c / 3u;
 
        points.resize(c);
        memcpy(&points[0], controls, sizeof(Vector3) * c);
 
        index_lo = 0;
        index_hi = t - 1;
        //mov_assert(points.size() % 3 == 0);
    }
 
    void SplineBase::clear()
    {
        index_lo = 0;
        index_hi = 0;
        points.clear();
    }
 
    std::string SplineBase::ToString() const
    {
        std::stringstream str;
        const char* mode_str[ModesEnd] = { "Linear", "CatmullRom", "Bezier3", "Uninitialized" };
 
        index_type count = this->points.size();
        str << "mode: " << mode_str[mode()] << std::endl;
        str << "points count: " << count << std::endl;
        for (index_type i = 0; i < count; ++i)
            str << "point " << i << " : " << points[i].toString() << std::endl;
 
        return str.str();
    }
 
}