source: downloads/ogre/OgreMain/src/OgreSimpleSpline.cpp @ 44

/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2006 Torus Knot Software Ltd
Also see acknowledgements in Readme.html

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser 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 Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 59 Temple
Place - Suite 330, Boston, MA 02111-1307, USA, or go to
http://www.gnu.org/copyleft/lesser.txt.

You may alternatively use this source under the terms of a specific version of
the OGRE Unrestricted License provided you have obtained such a license from
Torus Knot Software Ltd.
-----------------------------------------------------------------------------
*/
#include "OgreStableHeaders.h"
#include "OgreSimpleSpline.h"
#include "OgreVector4.h"
#include "OgreMatrix4.h"



namespace Ogre {

    //---------------------------------------------------------------------
    SimpleSpline::SimpleSpline()
    {
        // Set up matrix
        // Hermite polynomial
        mCoeffs[0][0] = 2;
        mCoeffs[0][1] = -2;
        mCoeffs[0][2] = 1;
        mCoeffs[0][3] = 1;
        mCoeffs[1][0] = -3;
        mCoeffs[1][1] = 3;
        mCoeffs[1][2] = -2;
        mCoeffs[1][3] = -1;
        mCoeffs[2][0] = 0;
        mCoeffs[2][1] = 0;
        mCoeffs[2][2] = 1;
        mCoeffs[2][3] = 0;
        mCoeffs[3][0] = 1;
        mCoeffs[3][1] = 0;
        mCoeffs[3][2] = 0;
        mCoeffs[3][3] = 0;

        mAutoCalc = true;
    }
    //---------------------------------------------------------------------
    SimpleSpline::~SimpleSpline()
    {
    }
    //---------------------------------------------------------------------
    void SimpleSpline::addPoint(const Vector3& p)
    {
        mPoints.push_back(p);
        if (mAutoCalc)
        {
            recalcTangents();
        }
    }
    //---------------------------------------------------------------------
    Vector3 SimpleSpline::interpolate(Real t)
    {
        // Currently assumes points are evenly spaced, will cause velocity
        // change where this is not the case
        // TODO: base on arclength?

        
        // Work out which segment this is in
        Real fSeg = t * (mPoints.size() - 1);
        unsigned int segIdx = (unsigned int)fSeg;
        // Apportion t 
        t = fSeg - segIdx;

        return interpolate(segIdx, t);

    }
    //---------------------------------------------------------------------
    Vector3 SimpleSpline::interpolate(unsigned int fromIndex, Real t)
    {
        // Bounds check
        assert (fromIndex < mPoints.size() &&
            "fromIndex out of bounds");

        if ((fromIndex + 1) == mPoints.size())
        {
            // Duff request, cannot blend to nothing
            // Just return source
            return mPoints[fromIndex];

        }

        // Fast special cases
        if (t == 0.0f)
        {
            return mPoints[fromIndex];
        }
        else if(t == 1.0f)
        {
            return mPoints[fromIndex + 1];
        }

        // Real interpolation
        // Form a vector of powers of t
        Real t2, t3;
        t2 = t * t;
        t3 = t2 * t;
        Vector4 powers(t3, t2, t, 1);


        // Algorithm is ret = powers * mCoeffs * Matrix4(point1, point2, tangent1, tangent2)
        Vector3& point1 = mPoints[fromIndex];
        Vector3& point2 = mPoints[fromIndex+1];
        Vector3& tan1 = mTangents[fromIndex];
        Vector3& tan2 = mTangents[fromIndex+1];
        Matrix4 pt;

        pt[0][0] = point1.x;
        pt[0][1] = point1.y;
        pt[0][2] = point1.z;
        pt[0][3] = 1.0f;
        pt[1][0] = point2.x;
        pt[1][1] = point2.y;
        pt[1][2] = point2.z;
        pt[1][3] = 1.0f;
        pt[2][0] = tan1.x;
        pt[2][1] = tan1.y;
        pt[2][2] = tan1.z;
        pt[2][3] = 1.0f;
        pt[3][0] = tan2.x;
        pt[3][1] = tan2.y;
        pt[3][2] = tan2.z;
        pt[3][3] = 1.0f;

        Vector4 ret = powers * mCoeffs * pt;


        return Vector3(ret.x, ret.y, ret.z);




    }
    //---------------------------------------------------------------------
    void SimpleSpline::recalcTangents(void)
    {
        // Catmull-Rom approach
        // 
        // tangent[i] = 0.5 * (point[i+1] - point[i-1])
        //
        // Assume endpoint tangents are parallel with line with neighbour

        size_t i, numPoints;
        bool isClosed;

        numPoints = mPoints.size();
        if (numPoints < 2)
        {
            // Can't do anything yet
            return;
        }

        // Closed or open?
        if (mPoints[0] == mPoints[numPoints-1])
        {
            isClosed = true;
        }
        else
        {
            isClosed = false;
        }

        mTangents.resize(numPoints);



        for(i = 0; i < numPoints; ++i)
        {
            if (i ==0)
            {
                // Special case start
                if (isClosed)
                {
                    // Use numPoints-2 since numPoints-1 is the last point and == [0]
                    mTangents[i] = 0.5 * (mPoints[1] - mPoints[numPoints-2]);
                }
                else
                {
                    mTangents[i] = 0.5 * (mPoints[1] - mPoints[0]);
                }
            }
            else if (i == numPoints-1)
            {
                // Special case end
                if (isClosed)
                {
                    // Use same tangent as already calculated for [0]
                    mTangents[i] = mTangents[0];
                }
                else
                {
                    mTangents[i] = 0.5 * (mPoints[i] - mPoints[i-1]);
                }
            }
            else
            {
                mTangents[i] = 0.5 * (mPoints[i+1] - mPoints[i-1]);
            }
            
        }



    }
    //---------------------------------------------------------------------
    const Vector3& SimpleSpline::getPoint(unsigned short index) const
    {
        assert (index < mPoints.size() && "Point index is out of bounds!!");

        return mPoints[index];
    }
    //---------------------------------------------------------------------
    unsigned short SimpleSpline::getNumPoints(void) const
    {
        return (unsigned short)mPoints.size();
    }
    //---------------------------------------------------------------------
    void SimpleSpline::clear(void)
    {
        mPoints.clear();
        mTangents.clear();
    }
    //---------------------------------------------------------------------
    void SimpleSpline::updatePoint(unsigned short index, const Vector3& value)
    {
        assert (index < mPoints.size() && "Point index is out of bounds!!");

        mPoints[index] = value;
        if (mAutoCalc)
        {
            recalcTangents();
        }
    }
    //---------------------------------------------------------------------
    void SimpleSpline::setAutoCalculate(bool autoCalc)
    {
        mAutoCalc = autoCalc;
    }




}