SuperellipseGenerator.cpp

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*/
 
#include "SuperellipseGenerator.hpp"
 
SuperellipseGenerator::SuperellipseGenerator(unsigned numPoints,
                                             double ellipseExponent,
                                             double width,
                                             double height,
                                             double botLeftX,
                                             double botLeftY)
        : mTargetNodeSpacing(DOUBLE_UNSET),
          mHeightOfTopSurface(0.3 * height)
{
    // Validate input
    assert(numPoints > 1);
    assert(ellipseExponent > 0.0);
    assert(width > 0.0);
    assert(height > 0.0);
 
    // Set up member variables
    mPoints.resize(numPoints);
 
    /*
     * Run a high-density pass around the parametric curve first
     */
    unsigned dense_pts = 50000;
 
    // Vectors to store information from the loop
    std::vector<double> cumulative_arc_length(dense_pts);
    std::vector<c_vector<double, 2> > dense_locations(dense_pts);
 
    // Helper variables for the loop
    double dense_spacing = (2.0 * M_PI) / (double)dense_pts;
    double cumulative_dist = 0.0;
    double temp_sin, temp_cos;
 
    // Fill in first location by hand
    cumulative_arc_length[0] = 0.0;
    dense_locations[0][0] = width * 0.5;
    dense_locations[0][1] = 0.0;
 
    // Fill in all other locations
    for (unsigned point = 1; point < dense_pts; point++)
    {
        // Update cumulative distance
        cumulative_dist += dense_spacing;
 
        // Get the current sin and cos values
        temp_cos = cos(cumulative_dist);
        temp_sin = sin(cumulative_dist);
 
        // x and y are powers of cos and sin, with the sign of sin and cos
        dense_locations[point][0] = copysign(pow(fabs(temp_cos), ellipseExponent), temp_cos) * width * 0.5;
        dense_locations[point][1] = copysign(pow(fabs(temp_sin), ellipseExponent), temp_sin) * height * 0.5;
 
        // Check that the new point created lies within [-width/2, width/2] x [-height/2, height/2]
        assert(fabs(dense_locations[point][0]) < width * 0.5 + 1e-10);
        assert(fabs(dense_locations[point][1]) < height * 0.5 + 1e-10);
 
        // Fill in arc length property
        cumulative_arc_length[point] = cumulative_arc_length[point - 1] + norm_2(dense_locations[point] - dense_locations[point - 1]);
    }
 
    double total_arc_length = cumulative_arc_length[dense_pts - 1] + norm_2(dense_locations[dense_pts - 1] - dense_locations[0]);
 
    // Since our perimeter is periodic, we get back to the start
    cumulative_arc_length.push_back(total_arc_length);
    dense_locations.push_back(dense_locations[0]);
 
    /*
     * Decide on the best place to put the actual boundary points
     */
 
    // Helper variables for loop
    unsigned dense_it = 0;
 
    mTargetNodeSpacing = total_arc_length / double(numPoints);
 
    double target_arclength = 0.0;
    double interpolant;
 
    // Fill in first point by hand
    mPoints[0] = dense_locations[0];
 
    // Fill in all other locations
    for (unsigned point = 1; point < numPoints; point++)
    {
        target_arclength = double(point) * mTargetNodeSpacing;
 
        while (cumulative_arc_length[dense_it] < target_arclength && dense_it < dense_pts)
        {
            dense_it ++;
        }
 
        // Check we're one position either side of the target arclength
        assert(cumulative_arc_length[dense_it - 1] < target_arclength);
        assert(cumulative_arc_length[dense_it] >= target_arclength);
 
        // Find the proportion between the two known locations we are
        interpolant = (target_arclength - cumulative_arc_length[dense_it - 1]) / (cumulative_arc_length[dense_it] - cumulative_arc_length[dense_it - 1]);
 
        // Calculate the location of the new point
        mPoints[point] = (1.0 - interpolant) * dense_locations[dense_it - 1] + interpolant * dense_locations[dense_it];
    }
 
    /*
     * If the exponent is at least 1, we return the default value which is the y-coord with largest value.
     *
     * If the exponent is less than 1, the top surface is defined as the height at which maximum curvature is attained.
     * We loop through the points looking at the change in x and change in y from the previous point.  The first
     * difference in which the absolute change in x is greater than the absolute change in y will be the point with
     * maximal curvature, for a superellipse.
     */
    if (ellipseExponent < 1.0)
    {
        double delta_x = fabs(mPoints[0][0] - mPoints[1][0]);
        double delta_y = fabs(mPoints[0][1] - mPoints[1][1]);
 
        // The following should always hold, for an exponent less than 1.0
        if (delta_x > delta_y)
        {
            NEVER_REACHED;
        }
 
        for (unsigned i = 1; i < numPoints; i++)
        {
            delta_x = fabs(mPoints[i][0] - mPoints[i - 1][0]);
            delta_y = fabs(mPoints[i][1] - mPoints[i - 1][1]);
 
            if (delta_x > delta_y)
            {
                mHeightOfTopSurface = 0.5 * (mPoints[i][1] + mPoints[i - 1][1]);
 
                break;
            }
 
            // We should meet this condition before being half way through the list
            if (i == unsigned(numPoints / 2.0))
            {
                NEVER_REACHED;
            }
        }
    }
 
    /*
     * Rescale all points to match parameters
     */
 
    // Move perimeter from [-width/2, width/2] x [-height/2, height/2] to correct location
    c_vector<double, 2> offset;
    offset[0] = width * 0.5 + botLeftX;
    offset[1] = height * 0.5 + botLeftY;
 
    // Reposition the height of the top surface
    mHeightOfTopSurface += offset[1];
 
    for (unsigned point = 0; point < numPoints; point++)
    {
        // Reposition all points
        mPoints[point] += offset;
 
        // Check we're in the right place
        assert((mPoints[point][0] > botLeftX - 1e-10) && (mPoints[point][0] < botLeftX + width + 1e-10));
        assert((mPoints[point][1] > botLeftY - 1e-10) && (mPoints[point][1] < botLeftY + height + 1e-10));
    }
}
 
SuperellipseGenerator::~SuperellipseGenerator()
{
    mPoints.clear();
}
 
double SuperellipseGenerator::GetTargetNodeSpacing()
{
    return mTargetNodeSpacing;
}
 
double SuperellipseGenerator::GetHeightOfTopSurface()
{
    return mHeightOfTopSurface;
}
 
const std::vector<c_vector<double, 2> > SuperellipseGenerator::GetPointsAsVectors() const
{
    return mPoints;
}
 
const std::vector<ChastePoint<2> > SuperellipseGenerator::GetPointsAsChastePoints() const
{
    std::vector<ChastePoint<2> > chaste_points;
 
    for (unsigned point = 0; point < mPoints.size(); point++)
    {
        chaste_points.push_back(ChastePoint<2>(mPoints[point]));
    }
 
    return chaste_points;
}