Spline.cpp

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/*
 * This file is part of the TrinityCore Project. See AUTHORS file for Copyright information
 *
 * This program is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the
 * Free Software Foundation; either version 2 of the License, or (at your
 * option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
 * more details.
 *
 * You should have received a copy of the GNU General Public License along
 * with this program. If not, see <http://www.gnu.org/licenses/>.
 */
 
#include "Spline.h"
#include <sstream>
#include <G3D/Matrix4.h>
 
namespace Movement{
 
SplineBase::EvaluationMethtod SplineBase::evaluators[SplineBase::ModesEnd] =
{
 &SplineBase::EvaluateLinear,
 &SplineBase::EvaluateCatmullRom,
 &SplineBase::EvaluateBezier3,
 &SplineBase::UninitializedSplineEvaluationMethod,
};
 
SplineBase::EvaluationMethtod SplineBase::derivative_evaluators[SplineBase::ModesEnd] =
{
 &SplineBase::EvaluateDerivativeLinear,
 &SplineBase::EvaluateDerivativeCatmullRom,
 &SplineBase::EvaluateDerivativeBezier3,
 &SplineBase::UninitializedSplineEvaluationMethod,
};
 
SplineBase::SegLenghtMethtod SplineBase::seglengths[SplineBase::ModesEnd] =
{
 &SplineBase::SegLengthLinear,
 &SplineBase::SegLengthCatmullRom,
 &SplineBase::SegLengthBezier3,
 &SplineBase::UninitializedSplineSegLenghtMethod,
};
 
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,
 &SplineBase::UninitializedSplineInitMethod,
};
 
 
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(Vector3 const* vertice, float t, Matrix4 const& 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(Vector3 const* vertice, float t, Matrix4 const& 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;
 float length = 0;
 while (i <= stepsPerSegment)
 {
 C_Evaluate(p, float(i) / float(stepsPerSegment), 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;
 float length = 0;
 while (i <= stepsPerSegment)
 {
 C_Evaluate(p, float(i) / float(stepsPerSegment), s_Bezier3Coeffs, nextPos);
 length += (nextPos - curPos).length();
 curPos = nextPos;
 ++i;
 }
 return length;
}
 
void SplineBase::init_spline(const Vector3 * controls, index_type count, EvaluationMode m, float orientation)
{
 m_mode = m;
 cyclic = false;
 initialOrientation = orientation;
 
 (this->*initializers[m_mode])(controls, count, 0);
}
 
void SplineBase::init_cyclic_spline(const Vector3 * controls, index_type count, EvaluationMode m, index_type cyclic_point, float orientation)
{
 m_mode = m;
 cyclic = true;
 initialOrientation = orientation;
 
 (this->*initializers[m_mode])(controls, count, cyclic_point);
}
 
void SplineBase::InitLinear(Vector3 const* controls, index_type count, 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(Vector3 const* controls, index_type count, 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] - G3D::Vector3{ std::cos(initialOrientation), std::sin(initialOrientation), 0.0f };
 
 points[high_index+1] = controls[cyclic_point];
 points[high_index+2] = controls[cyclic_point+1];
 }
 else
 {
 points[0] = controls[0] - G3D::Vector3{ std::cos(initialOrientation), std::sin(initialOrientation), 0.0f };
 points[high_index+1] = controls[count-1];
 }
 
 index_lo = lo_index;
 index_hi = high_index + (cyclic ? 1 : 0);
}
 
void SplineBase::InitBezier3(Vector3 const* controls, index_type count, 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);
}
 
SplineBase::SplineBase(): index_lo(0), index_hi(0), m_mode(UninitializedMode), cyclic(false), initialOrientation(0.f)
{
}
 
SplineBase::~SplineBase() = default;
 
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();
}
 
}