private Matrix4x4 mProjection; //投影矩阵
public Form1()
{
InitializeComponent();
mScale = new Matrix4x4();
mRotationX = new Matrix4x4();
mRotationY = new Matrix4x4();
mRotationZ = new Matrix4x4();
mView = new Matrix4x4();
mProjection = new Matrix4x4();
//初始化缩放矩阵
mScale[1, 1] = 250;
mScale[2, 2] = 250;
mScale[3, 3] = 250;
mScale[4, 4] = 1;
//初始化视图矩阵
mView[1, 1] = 1;
mView[2, 2] = 1;
mView[3, 3] = 1;
mView[4, 3] = camDistance; //相机距离
mView[4, 4] = 1;
//初始化投影矩阵
mProjection[1, 1] = 1;
mProjection[2, 2] = 1;
mProjection[3, 3] = 1;
mProjection[3, 4] = 1f / camDistance;
}
/// <summary>
/// 计算光照
/// </summary>
/// <param name="obj2World">模型矩阵</param>
/// <param name="light">光方向</param>
public void CalculateLighting(Matrix4x4 obj2World, Vector4 light)
{
// 应用模型矩阵，转换到世界坐标
Transform(obj2World);
//求两个边
Vector4 u = b - a;
Vector4 v = c - a;
//叉乘得法向量
normal = u.Cross(v);
//标准化法向量和灯光向量
Vector4 normalNor = normal.Normalized;
Vector4 lightNor = light.Normalized;
//计算灯光和法向量的点积
dot = normalNor.Dot(lightNor);
//限制在0-1范围
dot = Math.Max(0, dot);
//视线向量，z的反方向
Vector4 sight = new Vector4(0, 0, -1, 0);
//计算是否背面剔除
cullBack = normalNor.Dot(sight) < 0;
}
/// <summary>
/// 计算光照
/// </summary>
/// <param name="obj2World">模型矩阵</param>
/// <param name="light">光方向</param>
public void CalculateLighting(Matrix4x4 obj2World, Vector4 light)
{
foreach (Triangle3D t in triangles)
{
t.CalculateLighting(obj2World, light);
}
}
private void timer1_Tick(object sender, EventArgs e)
{
// 角度变化
angle += 3;
double rAngle = angle / 360f * Math.PI;
// 更新绕x旋转矩阵
mRotationX[1, 1] = 1;
mRotationX[2, 2] = Math.Cos(rAngle);
mRotationX[2, 3] = Math.Sin(rAngle);
mRotationX[3, 2] = -Math.Sin(rAngle);
mRotationX[3, 3] = Math.Cos(rAngle);
mRotationX[4, 4] = 1;
// 更新绕y旋转矩阵
mRotationY[1, 1] = Math.Cos(rAngle);
mRotationY[1, 3] = Math.Sin(rAngle);
mRotationY[2, 2] = 1;
mRotationY[3, 1] = -Math.Sin(rAngle);
mRotationY[3, 3] = Math.Cos(rAngle);
mRotationY[4, 4] = 1;
//// 更新绕z旋转矩阵
mRotationZ[1, 1] = Math.Cos(rAngle);
mRotationZ[1, 2] = Math.Sin(rAngle);
mRotationZ[2, 1] = -Math.Sin(rAngle);
mRotationZ[2, 2] = Math.Cos(rAngle);
mRotationZ[3, 3] = 1;
mRotationZ[4, 4] = 1;
//撤销X轴旋转效果
if (checkBox_x.Checked)
{
//乘以转置矩阵等效于乘以逆矩阵
Matrix4x4 tx = mRotationX.Transpose();
mRotationX = mRotationX.Mul(tx);
}
//撤销Y轴旋转效果
if (checkBox_y.Checked)
{
//乘以转置矩阵等效于乘以逆矩阵
Matrix4x4 ty = mRotationY.Transpose();
mRotationY = mRotationY.Mul(ty);
}
//撤销Z轴旋转效果
if (checkBox_z.Checked)
{
//乘以转置矩阵等效于乘以逆矩阵
Matrix4x4 tz = mRotationZ.Transpose();
mRotationZ = mRotationZ.Mul(tz);
}
Matrix4x4 mall = mRotationX.Mul(mRotationY.Mul(mRotationZ));
// 组合模型矩阵
Matrix4x4 m = mScale.Mul(mall);
if (drawCube){
cube.CalculateLighting(m, new Vector4(-1, 1, -1, 0));
}
else{
triangle3D.CalculateLighting(m, new Vector4(-1, 1, -1, 0));
}
// 应用视图矩阵
Matrix4x4 mv = m.Mul(mView);
// 应用投影矩阵
Matrix4x4 mvp = mv.Mul(mProjection);
// 应用变换矩阵
if (drawCube){
cube.Transform(mvp);
}
else{
triangle3D.Transform(mvp);
}
this.Invalidate();
}
/// <summary>
/// 三角形利用矩阵的乘法进行变换
/// </summary>
/// <param name="m">变换矩阵的组合</param>
public void Transform(Matrix4x4 m)
{
a = m.Mul(A);
b = m.Mul(B);
c = m.Mul(C);
}
/// <summary>
/// 矩阵变换
/// </summary>
public void Transform(Matrix4x4 m)
{
foreach (Triangle3D t in triangles){
t.Transform(m);
}
}