ShephardsPlayApplet/Misc.prejava at master · donhatch/ShephardsPlayApplet · GitHub

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#include "macros.h"

// TODO: what is this file? is it used anywhere??

import com.donhatchsw.util.CSG;
import com.donhatchsw.util.VecMath;
import com.donhatchsw.compat.Format;

final public class Misc
{
    private Misc(){ throw new AssertionError(); } // non-instantiatable util class

    // Assumes sp is platonic
    public static double circumconeCurvature(CSG.SPolytope sp)
    {
        // Take the angle between vertex-to-cell-center
        // and same-vertex-to-edge-center.
        CHECK_EQ(sp.p.dim, 3);
        CSG.SPolytope face = sp.p.facets[0];
        CSG.SPolytope edge = face.p.facets[0];
        CSG.SPolytope vertex = edge.p.facets[0];
        double cellCenter[] = CSG.cgOfVerts(sp.p);
        double faceCenter[] = CSG.cgOfVerts(face.p);
        double edgeCenter[] = CSG.cgOfVerts(edge.p);
        double vertexCenter[] = CSG.cgOfVerts(vertex.p);
        double angle = VecMath.angleBetweenUnitVectors(
                      VecMath.normalize(VecMath.vmv(cellCenter,vertexCenter)),
                      VecMath.normalize(VecMath.vmv(edgeCenter,vertexCenter)));
        double frac = Math.sin(angle);
        return 2*Math.PI*(1-frac);
    }
    // Assumes sp is platonic
    public static double vertexCurvature(CSG.SPolytope sp)
    {
        // Take a vertex.
        // Add up all the interior angles of faces at that vertex.
        // Subtract the result from 2*pi.
        CSG.SPolytope face = sp.p.facets[0];
        CSG.SPolytope edge = face.p.facets[0];
        CSG.SPolytope vertex = edge.p.facets[0];
        double cellCenter[] = CSG.cgOfVerts(sp.p);
        double faceCenter[] = CSG.cgOfVerts(face.p);
        double edgeCenter[] = CSG.cgOfVerts(edge.p);
        double vertexCenter[] = CSG.cgOfVerts(vertex.p);
        double angle = VecMath.angleBetweenUnitVectors(
                      VecMath.normalize(VecMath.vmv(faceCenter,vertexCenter)),
                      VecMath.normalize(VecMath.vmv(edgeCenter,vertexCenter)));
        int vertexValence = sp.p.getAllIncidences()[0][0][1].length;
        return 2*Math.PI - vertexValence*2*angle;
    }
    // Assumes sp is platonic
    public static double inconeCurvature(CSG.SPolytope sp)
    {
        // Take the angle between vertex-to-cell-center
        // and same-vertex-to-face-center.
        CHECK_EQ(sp.p.dim, 3);
        CSG.SPolytope face = sp.p.facets[0];
        CSG.SPolytope edge = face.p.facets[0];
        CSG.SPolytope vertex = edge.p.facets[0];
        double cellCenter[] = CSG.cgOfVerts(sp.p);
        double faceCenter[] = CSG.cgOfVerts(face.p);
        double edgeCenter[] = CSG.cgOfVerts(edge.p);
        double vertexCenter[] = CSG.cgOfVerts(vertex.p);
        double angle = VecMath.angleBetweenUnitVectors(
                      VecMath.normalize(VecMath.vmv(cellCenter,vertexCenter)),
                      VecMath.normalize(VecMath.vmv(faceCenter,vertexCenter)));
        double frac = Math.sin(angle);
        return 2*Math.PI*(1-frac);
    }
    public static double circumconeCurvature(double p, double q)
    {
        //double angle = Math.asin(Math.sin(Math.PI/2*(p-2)/p)/Math.sin(Math.PI/q));
        //double frac = Math.sin(angle);
        double frac = Math.sin(Math.PI/2*(p-2)/p)/Math.sin(Math.PI/q);
        return 2*Math.PI*(1-frac);
    }
    public static double vertexCurvature(double p, double q)
    {
        return 2*Math.PI - q*(Math.PI*(p-2)/p);
    }
    public static double inconeCurvature(double p, double q)
    {
        //double angle = Math.asin(Math.tan(Math.PI/2*(p-2)/p)/Math.tan(Math.PI/q));
        //double frac = Math.sin(angle);
        double frac = Math.tan(Math.PI/2*(p-2)/p)/Math.tan(Math.PI/q);
        return 2*Math.PI*(1-frac);
    }

    public static void printPlatonicSolidVertexCurvatures()
    {
        {
            int schlaflis[][] = {
                {3,3},
                {4,3},
                {3,4},
                {5,3},
                {3,5},
            };
            FORI (i, schlaflis.length)
            {
                int schlafli[] = schlaflis[i];
                CSG.SPolytope sp = CSG.makeRegularPolytope(schlafli);

                System.out.println("    {"+schlafli[0]+","+schlafli[1]+"}"
                                  +"  circumcone curvature = "+Format.sprintf("%.17g", RTOD(circumconeCurvature(sp)))
                                  +"  vertex curvature = "+Format.sprintf("%.17g", RTOD(vertexCurvature(sp)))
                                  +"  incone curvature = "+Format.sprintf("%.17g", RTOD(inconeCurvature(sp)))+"");
            }
            System.out.println();
        }
        {
            double schlaflis[][] = {
                {3,3},
                {4,3},
                {3,4},
                {5,3},
                {3,5},
                {5.5,3},
                {5.9,3},
                {5.99,3},
                {5.999,3},
                {5.9999,3},
                {5.99999,3},
                {5.999999,3},
                {5.9999999,3},
                {5.99999999,3},
                {5.999999999,3},
                {5.9999999999,3},
                {5.99999999999,3},
            };
            FORI (i, schlaflis.length)
            {
                double schlafli[] = schlaflis[i];
                double p = schlafli[0];
                double q = schlafli[1];
                System.out.println("    {"+p+","+q+"}"
                                  +"  circumcone curvature = "+Format.sprintf("%.17g", RTOD(circumconeCurvature(p,q)))
                                  +"  vertex curvature = "+Format.sprintf("%.17g", RTOD(vertexCurvature(p,q)))
                                  +"  incone curvature = "+Format.sprintf("%.17g", RTOD(inconeCurvature(p,q)))+"");
            }
            System.out.println();
        }


    } // printPlatonicSolidVertexCurvatures

    public static void main(String args[])
    {
        printPlatonicSolidVertexCurvatures();
    }

} // class Misc