Flower

using System;
using System.Collections.Generic;

using Ephere.Geometry;

/// Source: http://demonstrations.wolfram.com/VirtualFlowersWithCrispatePetals/

namespace Flowers
{
    public static class FlowerUtils
    {
        public static PolygonMesh CreateFlower(double details, int innerSegments, double r0, double r1,
            double c, double d, double a1, double p, double growth, double aa, double b, double a)
        {
            const double tMax = 6.255;
            int silhouetteVertCount = (int)(tMax / details);
            int numVerts = innerSegments * silhouetteVertCount + 1;
            Vector3[] vertices = new Vector3[numVerts];
            vertices[vertices.Length - 1] = new Vector3(0, 0, 0);
            PolygonMesh.Polygon[] faces = new PolygonMesh.Polygon[numVerts - 1];

            double angleStep = 2 * Math.PI * details / tMax;

            for (int i = 0; i < silhouetteVertCount; i++)
            {
                double angle = i * angleStep;
                double radius = r0 + (r1 * Math.Pow(Math.Abs(Math.Sin(c * angle * 0.5)), d));
                double x = radius * Math.Cos(angle);
                double y = radius * Math.Sin(angle);
                double rad = Math.Pow(x, 2) + Math.Pow(y, 2);
                double z = (1 + rad) * a1 * Math.Sin(p * i);

                vertices[i] = new Vector3((float)x, (float)y, (float)z) * (float)growth;
            }

            if (innerSegments == 1)
                for (int i = 0; i < faces.Length; i++)
                    faces[i] = new PolygonMesh.Polygon(new int[] { vertices.Length - 1, i, (i + 1) % faces.Length });

            else
                for (int i = 0; i < innerSegments ; i++)
                {
                    float discount = (i + 1.25f) / (innerSegments + 1);

                    for (int j = 0; j < silhouetteVertCount; j++)
                    {
                        if (i < innerSegments - 1)
                            vertices[j + (i + 1) * silhouetteVertCount] = vertices[j] * discount;

                        int k = (i + 1) * silhouetteVertCount;
                        int l = i * silhouetteVertCount;

                        if (i == 0)
                            faces[j] = new PolygonMesh.Polygon(new int[] { vertices.Length - 1, k + j, ((j + 1) % silhouetteVertCount) + silhouetteVertCount});

                        else if (i < innerSegments - 1)
                            faces[i * silhouetteVertCount + j] = new PolygonMesh.Polygon(
                                new int[] { l + j, k + j, ((k + 1 + j) % silhouetteVertCount) + k, ((l + 1 + j) % silhouetteVertCount) + l });

                        else
                            faces[i * silhouetteVertCount + j] = new PolygonMesh.Polygon(
                                new int[] { l + j, j, (j + 1) % silhouetteVertCount, ((l + 1 + j) % silhouetteVertCount) + l });

                    }
                }

            for (int i = 0; i < vertices.Length; i++)
            {
                double dist = vertices[i].Length;
                vertices[i].z += (float)(aa * Math.Exp(-b * Math.Pow(dist, 1.5)) * Math.Pow(dist, a));
            }

            foreach (var face in faces)
                face.SmoothingGroup = 1;

            return new PolygonMesh(vertices, faces);
        }
    }
}