/SilverlightViewport/SilverlightViewport/Primitives3D/BezierPrimitive.cs

#region File Description

//-----------------------------------------------------------------------------

// BezierPrimitive.cs

//

// Microsoft XNA Community Game Platform

// Copyright (C) Microsoft Corporation. All rights reserved.

//-----------------------------------------------------------------------------

#endregion



#region Using Statements

using System;

using System.Diagnostics;

using Microsoft.Xna.Framework;

#endregion



namespace Primitives3D

{

    /// <summary>

    /// Base class for primitives that are made out of cubic bezier patches

    /// (a type of curved surface). This is used by the TeapotPrimitive.

    /// </summary>

    public abstract class BezierPrimitive : GeometricPrimitive

    {

        /// <summary>

        /// Creates indices for a patch that is tessellated at the specified level.

        /// </summary>

        protected void CreatePatchIndices(int tessellation, bool isMirrored)

        {

            int stride = tessellation + 1;



            for (int i = 0; i < tessellation; i++)

            {

                for (int j = 0; j < tessellation; j++)

                {

                    // Make a list of six index values (two triangles).

                    int[] indices =

                    {

                        i * stride + j,

                        (i + 1) * stride + j,

                        (i + 1) * stride + j + 1,



                        i * stride + j,

                        (i + 1) * stride + j + 1,

                        i * stride + j + 1,

                    };



                    // If this patch is mirrored, reverse the

                    // indices to keep the correct winding order.

                    if (isMirrored)

                    {

                        Array.Reverse(indices);

                    }



                    // Create the indices.

                    foreach (int index in indices)

                    {

                        AddIndex(CurrentVertex + index);

                    }

                }

            }

        }





        /// <summary>

        /// Creates vertices for a patch that is tessellated at the specified level.

        /// </summary>

        protected void CreatePatchVertices(Vector3[] patch, int tessellation, bool isMirrored)

        {

            Debug.Assert(patch.Length == 16);



            for (int i = 0; i <= tessellation; i++)

            {

                float ti = (float)i / tessellation;



                for (int j = 0; j <= tessellation; j++)

                {

                    float tj = (float)j / tessellation;



                    // Perform four horizontal bezier interpolations

                    // between the control points of this patch.

                    Vector3 p1 = Bezier(patch[0], patch[1], patch[2], patch[3], ti);

                    Vector3 p2 = Bezier(patch[4], patch[5], patch[6], patch[7], ti);

                    Vector3 p3 = Bezier(patch[8], patch[9], patch[10], patch[11], ti);

                    Vector3 p4 = Bezier(patch[12], patch[13], patch[14], patch[15], ti);



                    // Perform a vertical interpolation between the results of the

                    // previous horizontal interpolations, to compute the position.

                    Vector3 position = Bezier(p1, p2, p3, p4, tj);



                    // Perform another four bezier interpolations between the control

                    // points, but this time vertically rather than horizontally.

                    Vector3 q1 = Bezier(patch[0], patch[4], patch[8], patch[12], tj);

                    Vector3 q2 = Bezier(patch[1], patch[5], patch[9], patch[13], tj);

                    Vector3 q3 = Bezier(patch[2], patch[6], patch[10], patch[14], tj);

                    Vector3 q4 = Bezier(patch[3], patch[7], patch[11], patch[15], tj);



                    // Compute vertical and horizontal tangent vectors.

                    Vector3 tangentA = BezierTangent(p1, p2, p3, p4, tj);

                    Vector3 tangentB = BezierTangent(q1, q2, q3, q4, ti);



                    // Cross the two tangent vectors to compute the normal.

                    Vector3 normal = Vector3.Cross(tangentA, tangentB);



                    if (normal.Length() > 0.0001f)

                    {

                        normal.Normalize();



                        // If this patch is mirrored, we must invert the normal.

                        if (isMirrored)

                            normal = -normal;

                    }

                    else

                    {

                        // In a tidy and well constructed bezier patch, the preceding

                        // normal computation will always work. But the classic teapot

                        // model is not tidy or well constructed! At the top and bottom

                        // of the teapot, it contains degenerate geometry where a patch

                        // has several control points in the same place, which causes

                        // the tangent computation to fail and produce a zero normal.

                        // We 'fix' these cases by just hard-coding a normal that points

                        // either straight up or straight down, depending on whether we

                        // are on the top or bottom of the teapot. This is not a robust

                        // solution for all possible degenerate bezier patches, but hey,

                        // it's good enough to make the teapot work correctly!



                        if (position.Y > 0)

                            normal = Vector3.Up;

                        else

                            normal = Vector3.Down;

                    }



                    // Create the vertex.

                    AddVertex(position, normal);

                }

            }

        }





        /// <summary>

        /// Performs a cubic bezier interpolation between four scalar control

        /// points, returning the value at the specified time (t ranges 0 to 1).

        /// </summary>

        static float Bezier(float p1, float p2, float p3, float p4, float t)

        {

            return p1 * (1 - t) * (1 - t) * (1 - t) +

                   p2 * 3 * t * (1 - t) * (1 - t) +

                   p3 * 3 * t * t * (1 - t) +

                   p4 * t * t * t;

        }





        /// <summary>

        /// Performs a cubic bezier interpolation between four Vector3 control

        /// points, returning the value at the specified time (t ranges 0 to 1).

        /// </summary>

        static Vector3 Bezier(Vector3 p1, Vector3 p2, Vector3 p3, Vector3 p4, float t)

        {

            Vector3 result = new Vector3();



            result.X = Bezier(p1.X, p2.X, p3.X, p4.X, t);

            result.Y = Bezier(p1.Y, p2.Y, p3.Y, p4.Y, t);

            result.Z = Bezier(p1.Z, p2.Z, p3.Z, p4.Z, t);



            return result;

        }





        /// <summary>

        /// Computes the tangent of a cubic bezier curve at the specified time,

        /// when given four scalar control points.

        /// </summary>

        static float BezierTangent(float p1, float p2, float p3, float p4, float t)

        {

            return p1 * (-1 + 2 * t - t * t) +

                   p2 * (1 - 4 * t + 3 * t * t) +

                   p3 * (2 * t - 3 * t * t) +

                   p4 * (t * t);

        }





        /// <summary>

        /// Computes the tangent of a cubic bezier curve at the specified time,

        /// when given four Vector3 control points. This is used for calculating

        /// normals (by crossing the horizontal and vertical tangent vectors).

        /// </summary>

        static Vector3 BezierTangent(Vector3 p1, Vector3 p2,

                                     Vector3 p3, Vector3 p4, float t)

        {

            Vector3 result = new Vector3();



            result.X = BezierTangent(p1.X, p2.X, p3.X, p4.X, t);

            result.Y = BezierTangent(p1.Y, p2.Y, p3.Y, p4.Y, t);

            result.Z = BezierTangent(p1.Z, p2.Z, p3.Z, p4.Z, t);



            result.Normalize();



            return result;

        }

    }

}