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[ASP.net教程]UWP简单示例(二):快速开始你的3D编程


准备

  IDE:Visual Studio 2015

  了解并学习:SharpDx官方GitHub

  推荐Demo:SharpDX_D3D12HelloWorld

第一节 世界

  世界坐标系是一个特殊的坐标系,它建立了描述其他坐标系所需要的参考框架。

  世界坐标系

  从另一方面说,不能用更大的、外部的坐标系来描述世界坐标系

  关于世界坐标系的典型问题都是关于初始位置和环境的:

  • 每个物体的位置和方向
  • 摄像机的位置和方向
  • 世界中每一点的地形是什么(如山丘、建筑、湖泊等)
  • 一个物体从哪里来,到哪里去(NPC的运动策略)

  左、右手坐标系

  所有的2D坐标系是等价的,但3D坐标系有“手性”之分

  左、右手坐标系可以互相转换,最简单的方法是只翻转一个轴的符号

  传统的计算机图形学使用左手坐标系,而线性代数则倾向于使用右手坐标系

  SharpDx采用左手坐标系,即X轴由右向左,Y轴由下至上,Z轴由里至外

  SharpDx的世界有多大

  首先,这个世界是有限且离散的

  描述三维坐标需要使用SharpDx或System.Numerics命名空间下的Vector3类型

  Vector3表示一个三维向量,它的x,y,z分量都是float类型(单精度浮点数),我们知道float范围是-3.40E+38 ~ +3.40E+38

  而原子的直径是0.1nm级别,若以它作为基本单位,那么这个世界大约是一个边长6.80E+25公里的方盒(约71877亿光年)

  这个世界足够大了吗

  目前认为银河系直径是10~12万光年,宇宙可视直径是920亿光年

  单精度浮点数可精确到小数点后6位,即当前世界最小分辨率是10-6倍原子大小

  那么离散的float类型足以描述现实世界了吗?向您介绍计算机图形学第一准则,留给您思考:

  • 计算机图形学第一准则:近似原则如果它看上去是对的它就是对的:)
Imports SharpDX''' <summary>''' 表示一个三维世界''' </summary>Public Interface IWorld  ''' <summary>  ''' 模型顶点变换矩阵的数组  ''' </summary>  ''' <returns></returns>  Property ModelMatrix As Matrix()  ''' <summary>  ''' 更新模型顶点变换矩阵  ''' </summary>  Sub Update()End Interface

VB.NET-IWorld
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示一个三维世界/// </summary>public interface IWorld{  /// <summary>  /// 模型顶点变换矩阵的数组  /// </summary>  /// <returns></returns>  Matrix[] ModelMatrix { get; set; }  /// <summary>  /// 更新模型顶点变换矩阵  /// </summary>  void Update();}

C#-IWorld

第二节 物体

  在编程中,具有宏观形状、体积或质量的抽象对象。

  位置Location

  一个三维向量,它表示当前物体在世界坐标系中的绝对位置

  比例Scale

  一个三维向量,表示当前物体x,y,z轴缩放比例

  旋转Rotation

  通常物体角位移有欧拉角和四元数两种表示方式

  欧拉角:

  • 欧拉角有三个分量,偏航角Yaw、俯仰角Pitch、横滚角Roll
  • 给定方位的表达方式不唯一
  • 两个角度间求插值非常困难
  • 万向锁是一个底层问题,至今没有简单的解决方案

  四元数:

  • 四元数(Quaternion)有四个分量,它是一个超复数
  • 四元数能够平滑插值,但它比欧拉角多占用33.3%的存储空间
  • 多个四元数表示一系列旋转变换时,将它们相乘(而非直接相加)
  • 四元数“减法”,一个变换Q1到另一个变换Q2的差△Q等于Q1的逆乘以Q2(而非直接相减)
  • 通过标准化四元数确保它为单位大小,否则它将不合法
Imports SharpDX''' <summary>''' 表示一个可包含若干子对象的刚体''' </summary>Public Interface IRigidBody  ''' <summary>  ''' 子物体  ''' </summary>  ''' <returns></returns>  Property Children As List(Of IRigidBody)  ''' <summary>  ''' 父物体  ''' </summary>  ''' <returns></returns>  Property Parent As IRigidBody  ''' <summary>  ''' 位置  ''' </summary>  ''' <returns></returns>  Property Location As Vector3  ''' <summary>  ''' 缩放  ''' </summary>  ''' <returns></returns>  Property Scale As Vector3  ''' <summary>  ''' 旋转  ''' </summary>  ''' <returns></returns>  Property Qua As Quaternion  ''' <summary>  ''' 可见性  ''' </summary>  ''' <returns></returns>  Property Visible As Boolean  Sub Update()End Interface

VB.NET-IRigidBody
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示一个可包含若干子对象的刚体/// </summary>public interface IRigidBody{  /// <summary>  /// 子物体  /// </summary>  /// <returns></returns>  List<IRigidBody> Children { get; set; }  /// <summary>  /// 父物体  /// </summary>  /// <returns></returns>  IRigidBody Parent { get; set; }  /// <summary>  /// 位置  /// </summary>  /// <returns></returns>  Vector3 Location { get; set; }  /// <summary>  /// 缩放  /// </summary>  /// <returns></returns>  Vector3 Scale { get; set; }  /// <summary>  /// 旋转  /// </summary>  /// <returns></returns>  Quaternion Qua { get; set; }  /// <summary>  /// 可见性  /// </summary>  /// <returns></returns>  bool Visible { get; set; }  void Update();}

C#-IRigidBody

第三节 矩阵与线性变换

  线性变换总是把线性子空间变为线性子空间,但是维数可能降低。矩阵的本质就是描述线性变换。

  模型与世界空间

  物体最开始由物体空间来描述。其中常见的信息包括顶点位置和表面法向量

  可将坐标从物体空间转换到世界空间中,此过程称作模型变换

  通常,光照计算使用世界空间,其实光照计算只需确保几何体和光线在同一空间

  摄像机空间

  通过视变换,顶点从世界空间变换到摄像机空间,此空间也称作眼睛空间

  裁剪与屏幕空间

  裁剪空间又名标准视体空间,它是为透视投影做准备

  一旦用视锥完成了几何体裁剪,即可向屏幕空间投影

  ModelMatrix=World*View*Projection

  World=ScaleMatrix*RotationMatrix*TranslateMatrix:

  • 缩放矩阵 ScaleMatrix=Matrix.Scaling(Object.Scale)
  • 旋转矩阵 RotationMatrix=Matrix.RotationQuaternion(Object.Quaternion)
  • 平移矩阵 TranslateMatrix=Matrix.Translation(Object.Location)
  • 默认旋转中心是原点,所以这三者相乘的顺序不能变

  View=Matrix.LookAtLH(eye,target,up):

  • 眼睛位置 eye=New Vector3(0,0,100),表示当前摄像机位于Z轴100值处
  • 视点位置 target=New Vector3(0,0,0),表示当前摄像机看向3D空间的原点
  • 向上向量 up=Vector.UnitY,当前摄像机的向上方向
  • LH表示左手坐标系,Matrix.LookAtRH是用于右手坐标系

  Projection=Matrix.PerspectiveFovLH(fov, aspect, znear, zfar):

  • 视椎体水平角 fov=Math.PI/ 3.0F,即水平可视角范围,通常为60度
  • 视锥体宽高比 aspect=ScreenWidth/ScreenHeight,通常和屏幕宽高比一致
  • 近裁面深度值 znear=1,即最近可视范围,用户可自由设置
  • 远裁面深度值 zfar=10000,即最远可视范围,用户可自由设置
  • 实际上这是裁剪变换矩阵,投影到屏幕是由API完成的
Imports SharpDX''' <summary>''' 表示用于视变换的摄像机''' </summary>Public Interface ICamera  ''' <summary>  ''' 获取或设置摄像机位置  ''' </summary>  ''' <returns></returns>  Property Eye As Vector3  ''' <summary>  ''' 获取或设置目标视点位置  ''' </summary>  ''' <returns></returns>  Property Target As Vector3  ''' <summary>  ''' 获取或设置摄像机向上方向  ''' </summary>  ''' <returns></returns>  Property Up As Vector3  ''' <summary>  ''' 获取当前视变换矩阵  ''' </summary>  ''' <returns></returns>  ReadOnly Property View As MatrixEnd Interface

VB.NET-ICamera
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示用于视变换的摄像机/// </summary>public interface ICamera{  /// <summary>  /// 获取或设置摄像机位置  /// </summary>  /// <returns></returns>  Vector3 Eye { get; set; }  /// <summary>  /// 获取或设置目标视点位置  /// </summary>  /// <returns></returns>  Vector3 Target { get; set; }  /// <summary>  /// 获取或设置摄像机向上方向  /// </summary>  /// <returns></returns>  Vector3 Up { get; set; }  /// <summary>  /// 获取当前视变换矩阵  /// </summary>  /// <returns></returns>  Matrix View { get; }}

C#-ICamera

第四节 三角网格

  多边形网格用来模拟复杂物体的表面,任意多边形网格都能转成三角网格。

  表示网格

  多边形和三角网格在图形学和建模中广泛使用,最直接表示方法是用三角形数组

  三角网格需要存储三类信息:

  • 顶点 每个三角形都有三个顶点,各顶点都有可能和其他三角形共享
  • 边    连接两个顶点的边,每个三角形有三条边
  • 面    每个三角形对应一个面,我们可以用顶点或者边列表表示面

  索引三角网格

  在索引三角网格中,我们维护两个列表:顶点表和三角形表

  每个顶点包含一个3D位置,也可能有如纹理映射坐标、表面法向量、光照值等复杂数据

  每个三角形由顶点列表的三个索引组成

  顶点列出的顺序非常重要,它决定面是“正面”还是“反面”

  另外,表面法向量、纹理映射保存在三角形一级

  索引三角形列表中的邻接信息是隐含的,边信息不会被直接存储

  我们可以通过搜索三角形表找出公共边

  创建一个立方体

  一个立方体有6个矩形面,每个面有4个顶点

  一个矩形面由两个三角形组成

  可见我们共需要24个顶点,12个三角形

  假若不分开描述各面,8个顶点就足够描述一个六面体,但仍需要12个三角形

  ''' <summary>  ''' 表示一个顶点  ''' </summary>  Public Structure Vertex    Public Position As Vector3    Public Color As Vector4    Public Sub New(position As Vector3, color As Vector4)      Me.Position = position      Me.Color = color    End Sub  End Structure

VB.NET-Vertex
  ''' <summary>  ''' 返回一个指定长宽高的正六面体的顶点数组  ''' </summary>  Public Shared Function CreateCube(w As Single, h As Single, d As Single) As Vertex()    w = w / 2    h = h / 2    d = d / 2    Dim vertices As Vertex() = New Vertex() {      New Vertex(New Vector3(-w, h, d), New Vector4(0, 1, 0, 1)), New Vertex(New Vector3(w, h, d), New Vector4(0, 1, 0, 1)),      New Vertex(New Vector3(w, h, -d), New Vector4(0, 1, 0, 1)), New Vertex(New Vector3(-w, h, -d), New Vector4(0, 1, 0, 1)),      New Vertex(New Vector3(-w, -h, d), New Vector4(1, 0, 1, 1)), New Vertex(New Vector3(w, -h, d), New Vector4(1, 0, 1, 1)),      New Vertex(New Vector3(w, -h, -d), New Vector4(1, 0, 1, 1)), New Vertex(New Vector3(-w, -h, -d), New Vector4(1, 0, 1, 1)),      New Vertex(New Vector3(-w, -h, d), New Vector4(1, 0, 0, 1)), New Vertex(New Vector3(-w, h, d), New Vector4(1, 0, 0, 1)),      New Vertex(New Vector3(-w, h, -d), New Vector4(1, 0, 0, 1)), New Vertex(New Vector3(-w, -h, -d), New Vector4(1, 0, 0, 1)),      New Vertex(New Vector3(w, -h, d), New Vector4(1, 1, 0, 1)), New Vertex(New Vector3(w, h, d), New Vector4(1, 1, 0, 1)),      New Vertex(New Vector3(w, h, -d), New Vector4(1, 1, 0, 1)), New Vertex(New Vector3(w, -h, -d), New Vector4(1, 1, 0, 1)),      New Vertex(New Vector3(-w, h, d), New Vector4(0, 1, 1, 1)), New Vertex(New Vector3(w, h, d), New Vector4(0, 1, 1, 1)),      New Vertex(New Vector3(w, -h, d), New Vector4(0, 1, 1, 1)), New Vertex(New Vector3(-w, -h, d), New Vector4(0, 1, 1, 1)),      New Vertex(New Vector3(-w, h, -d), New Vector4(0, 0, 1, 1)), New Vertex(New Vector3(w, h, -d), New Vector4(0, 0, 1, 1)),      New Vertex(New Vector3(w, -h, -d), New Vector4(0, 0, 1, 1)), New Vertex(New Vector3(-w, -h, -d), New Vector4(0, 0, 1, 1))}    Return vertices  End Function

VB.NET-CreateCube
using SharpDx;/// <summary>/// 表示一个存储3D位置与颜色信息的顶点/// </summary>public struct Vertex{  public Vector3 Position;  public Vector4 Color;  public Vertex(Vector3 position, Vector4 color)  {    this.Position = position;    this.Color = color;  }}

C#-Vertex
/// <summary>/// 返回一个指定长宽高的正六面体的顶点数组/// </summary>public static Vertex[] CreateCube(float w, float h, float d){  w = w / 2;  h = h / 2;  d = d / 2;  Vertex[] vertices = new Vertex[] {    new Vertex(new Vector3(-w, h, d), new Vector4(0, 1, 0, 1)),    new Vertex(new Vector3(w, h, d), new Vector4(0, 1, 0, 1)),    new Vertex(new Vector3(w, h, -d), new Vector4(0, 1, 0, 1)),    new Vertex(new Vector3(-w, h, -d), new Vector4(0, 1, 0, 1)),    new Vertex(new Vector3(-w, -h, d), new Vector4(1, 0, 1, 1)),    new Vertex(new Vector3(w, -h, d), new Vector4(1, 0, 1, 1)),    new Vertex(new Vector3(w, -h, -d), new Vector4(1, 0, 1, 1)),    new Vertex(new Vector3(-w, -h, -d), new Vector4(1, 0, 1, 1)),    new Vertex(new Vector3(-w, -h, d), new Vector4(1, 0, 0, 1)),    new Vertex(new Vector3(-w, h, d), new Vector4(1, 0, 0, 1)),    new Vertex(new Vector3(-w, h, -d), new Vector4(1, 0, 0, 1)),    new Vertex(new Vector3(-w, -h, -d), new Vector4(1, 0, 0, 1)),    new Vertex(new Vector3(w, -h, d), new Vector4(1, 1, 0, 1)),    new Vertex(new Vector3(w, h, d), new Vector4(1, 1, 0, 1)),    new Vertex(new Vector3(w, h, -d), new Vector4(1, 1, 0, 1)),    new Vertex(new Vector3(w, -h, -d), new Vector4(1, 1, 0, 1)),    new Vertex(new Vector3(-w, h, d), new Vector4(0, 1, 1, 1)),    new Vertex(new Vector3(w, h, d), new Vector4(0, 1, 1, 1)),    new Vertex(new Vector3(w, -h, d), new Vector4(0, 1, 1, 1)),    new Vertex(new Vector3(-w, -h, d), new Vector4(0, 1, 1, 1)),    new Vertex(new Vector3(-w, h, -d), new Vector4(0, 0, 1, 1)),    new Vertex(new Vector3(w, h, -d), new Vector4(0, 0, 1, 1)),    new Vertex(new Vector3(w, -h, -d), new Vector4(0, 0, 1, 1)),    new Vertex(new Vector3(-w, -h, -d), new Vector4(0, 0, 1, 1))  };  return vertices;}

C#-CreateCube

第五节 方块人物

  可直接用一个骨骼模型描述生物外形,至少MineCraft是这样的。

  骨骼关系

  一个骨骼节点可以若干子骨骼,但只能有一个父骨骼

  易见我们可以用一个树形结构来描述骨骼系统

  父子骨骼间存在一种“联动”关系,比如我们移动右手手臂,右手也会跟随移动

  为体现这种“联动”,在编程中需要将作用于某个骨骼的的变换也同等作用于它的子骨骼

  人体骨骼方块

  上部(10块):头部、颈部、左右肩、左右上臂,左右下臂,左右手

  中部(2 块):胸部、腰部

  下部(8 块):左右骻、左右大腿,左右小腿和左右脚

  通常,腰部是根节点的较好选择

Imports SharpDX''' <summary>''' 表示骨骼结点''' </summary>Public Class Bone  Inherits RigidBodyBase  Public Overrides Property Qua As Quaternion    Set(value As Quaternion)      If IsNewQua Then        IsNewQua = False        sQua = value        sQua.Invert()        sQua.Normalize()      End If      mQua = value    End Set    Get      Return Quaternion.Normalize(sQua * mQua)    End Get  End Property  ''' <summary>  ''' 绝对坐标  ''' </summary>  Public AbsoluteLoc As Vector3  ''' <summary>  ''' 相对坐标  ''' </summary>  Public RelativeLoc As Vector3  ''' <summary>  ''' 父骨骼  ''' </summary>  Public ParentBone As Bone  ''' <summary>  ''' 骨骼相对旋转  ''' </summary>  Public BoneQua As New Quaternion(0, 0, 0, 1)  ''' <summary>  ''' 子骨骼  ''' </summary>  Public ChildrenBone As New List(Of Bone)  ''' <summary>  ''' 索引  ''' </summary>  Public Index As Integer  Private mQua As New Quaternion(0, 0, 0, 1)  Private sQua As New Quaternion(0, 0, 0, 1)  Private IsNewQua As Boolean = True  Public Sub New(loc As Vector3, scale As Vector3)    Me.RelativeLoc = loc * 10    Me.Scale = scale  End SubEnd Class

VB.NET-Bone
Imports SharpDX''' <summary>''' 表示一个用于描述骨骼信息的对象''' </summary>Public Class BoneInf  Public Loc As Vector3  Public Scale As Vector3  Public ParentIndex As Integer  Public ChildIndexArr() As Integer  Public Sub New(l As Vector3, s As Vector3, p As Integer, c As Integer())    Loc = New Vector3(l.Z, l.Y, l.X)    Scale = New Vector3(s.Z, s.Y, s.X)    ParentIndex = p    ChildIndexArr = c  End SubEnd Class

VB.NET-BoneInf
Imports SharpDX''' <summary>''' 表示一个人类模型''' </summary>Public Class Human  Inherits RigidBodyBase  Public RootBone As Bone  Dim BoneInfArr() As BoneInf = {                    New BoneInf(New Vector3(0, 0, 0), New Vector3(1, 1, 1), 0, New Integer() {1, 12, 16}),'腰部0                    New BoneInf(New Vector3(0, 5, 0), New Vector3(2.5, 5, 1), 0, New Integer() {2, 4, 8}),'胸部1                    New BoneInf(New Vector3(0, 1, 0), New Vector3(0.7, 1, 1), 1, New Integer() {3}),'颈部2                    New BoneInf(New Vector3(0, 1.5, 0), New Vector3(1.3, 1.5, 1), 2, New Integer() {}),'头部3                    New BoneInf(New Vector3(-2, 0, 0), New Vector3(2, 1, 1), 1, New Integer() {5}),'左肩4                    New BoneInf(New Vector3(0, -2.5, 0), New Vector3(1, 2.5, 1), 4, New Integer() {6}),'左上臂5                    New BoneInf(New Vector3(0, -2.5, 0), New Vector3(1, 2.5, 1), 5, New Integer() {7}),'左小臂6                    New BoneInf(New Vector3(0, -1, 0), New Vector3(1, 1, 1), 6, New Integer() {}),'左手7                    New BoneInf(New Vector3(2, 0, 0), New Vector3(2, 1, 1), 1, New Integer() {9}),'右肩8                    New BoneInf(New Vector3(0, -2.5, 0), New Vector3(1, 2.5, 1), 8, New Integer() {10}),'右上臂9                    New BoneInf(New Vector3(0, -2.5, 0), New Vector3(1, 2.5, 1), 9, New Integer() {11}),'右小臂10                    New BoneInf(New Vector3(0, -1, 0), New Vector3(1, 1, 1), 10, New Integer() {}),'右手11                    New BoneInf(New Vector3(-0.8, 0, 0), New Vector3(0.8, 1, 1), 0, New Integer() {13}),'左骻12                    New BoneInf(New Vector3(0, -4, 0), New Vector3(1, 4, 1), 12, New Integer() {14}),'左大腿13                    New BoneInf(New Vector3(0, -4, 0), New Vector3(1, 4, 1), 13, New Integer() {15}),'左小腿14                    New BoneInf(New Vector3(0, -1, 0), New Vector3(1, 1, 1), 14, New Integer() {}),'左脚15                    New BoneInf(New Vector3(0.8, 0, 0), New Vector3(0.8, 1, 1), 0, New Integer() {17}),'右骻16                    New BoneInf(New Vector3(0, -4, 0), New Vector3(1, 4, 1), 16, New Integer() {18}),'右大腿17                    New BoneInf(New Vector3(0, -4, 0), New Vector3(1, 4, 1), 17, New Integer() {19}),'右小腿18                    New BoneInf(New Vector3(0, -1, 0), New Vector3(1, 1, 1), 18, New Integer() {})'右脚19                    }  Public Sub New()    CreateBody()    CalcBone(RootBone)  End Sub  ''' <summary>  ''' 更新指定索引的骨骼  ''' </summary>  ''' <param name="qua">旋转</param>  ''' <param name="index">骨骼索引</param>  Public Sub UpdateBone(qua As Quaternion, index As Integer)    qua.Normalize()    DirectCast(Children(index), Bone).Qua = qua    CalcBone(DirectCast(Children(index), Bone).ParentBone)  End Sub  ''' <summary>  ''' 更新所有子骨骼  ''' </summary>  ''' <param name="parent"></param>  Private Sub CalcBone(parent As Bone)    For Each SubBone As Bone In parent.ChildrenBone      SubBone.BoneQua = Quaternion.Normalize(Me.Qua * SubBone.Qua)      Dim tempLoc = (Matrix.Translation(SubBone.RelativeLoc) * Matrix.RotationQuaternion(SubBone.BoneQua)).TranslationVector      SubBone.AbsoluteLoc = parent.AbsoluteLoc + tempLoc      SubBone.Location = parent.AbsoluteLoc + tempLoc / 2      CalcBone(SubBone)    Next  End Sub  ''' <summary>  ''' 创建人物身体的所有骨骼  ''' </summary>  Private Sub CreateBody()    For i = 0 To BoneInfArr.Count - 1      Children.Add(New Bone(BoneInfArr(i).Loc, BoneInfArr(i).Scale))      DirectCast(Children(i), Bone).Index = i    Next    For i = 0 To BoneInfArr.Count - 1      DirectCast(Children(i), Bone).ParentBone = Children(BoneInfArr(i).ParentIndex)      For Each SubIndex In BoneInfArr(i).ChildIndexArr        DirectCast(Children(i), Bone).ChildrenBone.Add(Children(SubIndex))      Next    Next    RootBone = DirectCast(Children(0), Bone)    RootBone.Parent = RootBone  End SubEnd Class

VB.NET-Human
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示骨骼结点/// </summary>public class Bone : RigidBodyBase{  public override Quaternion Qua {    get { return Quaternion.Normalize(sQua * mQua); }    set {      if (IsNewQua) {        IsNewQua = false;        sQua = value;        sQua.Invert();        sQua.Normalize();      }      mQua = value;    }  }  /// <summary>  /// 绝对坐标  /// </summary>  public Vector3 AbsoluteLoc;  /// <summary>  /// 相对坐标  /// </summary>  public Vector3 RelativeLoc;  /// <summary>  /// 父骨骼  /// </summary>  public Bone ParentBone;  /// <summary>  /// 骨骼相对旋转  /// </summary>  public Quaternion BoneQua = new Quaternion(0, 0, 0, 1);  /// <summary>  /// 子骨骼  /// </summary>  public List<Bone> ChildrenBone = new List<Bone>();  /// <summary>  /// 索引  /// </summary>  public int Index;  private Quaternion mQua = new Quaternion(0, 0, 0, 1);  private Quaternion sQua = new Quaternion(0, 0, 0, 1);  private bool IsNewQua = true;  public Bone(Vector3 loc, Vector3 scale)  {    this.RelativeLoc = loc * 10;    this.Scale = scale;  }}

C#-Bone
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示一个用于描述骨骼信息的对象/// </summary>public class BoneInf{  public Vector3 Loc;  public Vector3 Scale;  public int ParentIndex;  public int[] ChildIndexArr;  public BoneInf(Vector3 l, Vector3 s, int p, int[] c)  {    Loc = new Vector3(l.Z, l.Y, l.X);    Scale = new Vector3(s.Z, s.Y, s.X);    ParentIndex = p;    ChildIndexArr = c;  }}

C#-BoneInf
using System;using System.Collections;using System.Collections.Generic;using System.Data;using System.Diagnostics;using SharpDX;/// <summary>/// 表示一个人类模型/// </summary>public class Human : RigidBodyBase{  public Bone RootBone;  BoneInf[] BoneInfArr = {    new BoneInf(new Vector3(0, 0, 0), new Vector3(1, 1, 1), 0, new int[] {      1,      12,      16    }),    //腰部0    new BoneInf(new Vector3(0, 5, 0), new Vector3(2.5, 5, 1), 0, new int[] {      2,      4,      8    }),    //胸部1    new BoneInf(new Vector3(0, 1, 0), new Vector3(0.7, 1, 1), 1, new int[] { 3 }),    //颈部2    new BoneInf(new Vector3(0, 1.5, 0), new Vector3(1.3, 1.5, 1), 2, new int[]),    //头部3    new BoneInf(new Vector3(-2, 0, 0), new Vector3(2, 1, 1), 1, new int[] { 5 }),    //左肩4    new BoneInf(new Vector3(0, -2.5, 0), new Vector3(1, 2.5, 1), 4, new int[] { 6 }),    //左上臂5    new BoneInf(new Vector3(0, -2.5, 0), new Vector3(1, 2.5, 1), 5, new int[] { 7 }),    //左小臂6    new BoneInf(new Vector3(0, -1, 0), new Vector3(1, 1, 1), 6, new int[]),    //左手7    new BoneInf(new Vector3(2, 0, 0), new Vector3(2, 1, 1), 1, new int[] { 9 }),    //右肩8    new BoneInf(new Vector3(0, -2.5, 0), new Vector3(1, 2.5, 1), 8, new int[] { 10 }),    //右上臂9    new BoneInf(new Vector3(0, -2.5, 0), new Vector3(1, 2.5, 1), 9, new int[] { 11 }),    //右小臂10    new BoneInf(new Vector3(0, -1, 0), new Vector3(1, 1, 1), 10, new int[]),    //右手11    new BoneInf(new Vector3(-0.8, 0, 0), new Vector3(0.8, 1, 1), 0, new int[] { 13 }),    //左骻12    new BoneInf(new Vector3(0, -4, 0), new Vector3(1, 4, 1), 12, new int[] { 14 }),    //左大腿13    new BoneInf(new Vector3(0, -4, 0), new Vector3(1, 4, 1), 13, new int[] { 15 }),    //左小腿14    new BoneInf(new Vector3(0, -1, 0), new Vector3(1, 1, 1), 14, new int[]),    //左脚15    new BoneInf(new Vector3(0.8, 0, 0), new Vector3(0.8, 1, 1), 0, new int[] { 17 }),    //右骻16    new BoneInf(new Vector3(0, -4, 0), new Vector3(1, 4, 1), 16, new int[] { 18 }),    //右大腿17    new BoneInf(new Vector3(0, -4, 0), new Vector3(1, 4, 1), 17, new int[] { 19 }),    //右小腿18    new BoneInf(new Vector3(0, -1, 0), new Vector3(1, 1, 1), 18, new int[])    //右脚19  };  public Human()  {    CreateBody();    CalcBone(RootBone);  }  /// <summary>  /// 更新指定索引的骨骼  /// </summary>  /// <param name="qua">旋转</param>  /// <param name="index">骨骼索引</param>  public void UpdateBone(Quaternion qua, int index)  {    qua.Normalize();    ((Bone)Children(index)).Qua = qua;    CalcBone(((Bone)Children(index)).ParentBone);  }  /// <summary>  /// 更新所有子骨骼  /// </summary>  /// <param name="parent"></param>  private void CalcBone(Bone parent)  {    foreach (Bone SubBone in parent.ChildrenBone) {      SubBone.BoneQua = Quaternion.Normalize(this.Qua * SubBone.Qua);      dynamic tempLoc = (Matrix.Translation(SubBone.RelativeLoc) * Matrix.RotationQuaternion(SubBone.BoneQua)).TranslationVector;      SubBone.AbsoluteLoc = parent.AbsoluteLoc + tempLoc;      SubBone.Location = parent.AbsoluteLoc + tempLoc / 2;      CalcBone(SubBone);    }  }  /// <summary>  /// 创建人物身体的所有骨骼  /// </summary>  private void CreateBody()  {    for (i = 0; i <= BoneInfArr.Count - 1; i++) {      Children.Add(new Bone(BoneInfArr[i].Loc, BoneInfArr[i].Scale));      ((Bone)Children(i)).Index = i;    }    for (i = 0; i <= BoneInfArr.Count - 1; i++) {      ((Bone)Children(i)).ParentBone = Children(BoneInfArr[i].ParentIndex);      foreach (object SubIndex_loopVariable in BoneInfArr[i].ChildIndexArr) {        SubIndex = SubIndex_loopVariable;        ((Bone)Children(i)).ChildrenBone.Add(Children(SubIndex));      }    }    RootBone = (Bone)Children(0);    RootBone.Parent = RootBone;  }}

C#-Human

附录

  这是开始你的3D编程的第一步

  需要注意哪些问题?

  3D编程中,形式转换经常是错误的根源,尤其要注意坐标系的手性

  在限制欧拉角中,俯仰角Pitch的范围是±90º,偏航角Yaw的范围是±180º

  (额外说明一点,UWP的CompositeTransform3D使用的就是限制欧拉角)

  为什么选择SharpDx?

  SharpDx库与UWP兼容,其他如SharpGL不兼容

  如果你是C#开发者,Unity3D会是更好的选择

  Direct3D是底层的3D图形库,通过接触它你可以学习到很多底层图形编程知识

  了解底层知识会使你在接触并使用Unity3D等引擎时更加得心应手

  其它

  开源链接:ExperDot.SharpDx3DEngine

  参考书籍:《3D数学基础:图形与游戏开发》[美]Fletcher Dunnlan Parberry著 清华大学出版社(史银雪、陈洪和王荣静译)