//三角形利用矩阵乘法变换 传入变换矩阵
public void TransForm(Matrix4x4 m)
{
//为了避免 double 类型反复相乘的 数据精确度下降 每次都是用原始数据相乘
this.a = m.Mul(this.A);
this.b = m.Mul(this.B);
this.c = m.Mul(this.C);
}
public vector4(vector4 v)
{
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = v.w;
}
private void Form1_Load(object sender, EventArgs e)
{
vector4 a = new vector4(0, 0.5, 0, 1);//只有第四个点位1 矩阵乘法才成立 所以最后一位要求是1
vector4 b = new vector4(0.5, -0.5, 0, 1);
vector4 c = new vector4(-0.5, -0.5, 0, 1);
t = new Triangle3D(a, b, c);
}
/// <summary>
/// 把四维 点 转化为投影平面的 2D点
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
private PointF Get2DPointF(vector4 v)
{
PointF p = new PointF();
p.X = (float)(v.x / v.w);//透视除法 向量分量 除以 w分量
p.Y = -(float)(v.y / v.w);
return(p);
}
public vector4 Mul(vector4 v)
{
vector4 newV = new vector4();
newV.x = v.x * this[1, 1] + v.y * this[2, 1] + v.z * this[3, 1] + v.w * this[4, 1];
newV.y = v.x * this[1, 2] + v.y * this[2, 2] + v.z * this[3, 2] + v.w * this[4, 2];
newV.z = v.x * this[1, 3] + v.y * this[2, 3] + v.z * this[3, 3] + v.w * this[4, 3];
newV.w = v.x * this[1, 4] + v.y * this[2, 4] + v.z * this[3, 4] + v.w * this[4, 4];
return(newV);
}
//绘制三角形到2d 窗口上
//
public void CalculateLighting(Matrix4x4 _Object2world, vector4 L)
{
this.TransForm(_Object2world); //直接完成世界坐标的变换
vector4 U = this.b - this.a;
vector4 V = this.c - this.a;
vector4 normal = U.Cross(V);
dot = normal.Noralized.Dot(L.Noralized);//得到夹角
dot = Math.Max(0, dot);
vector4 E = new vector4(0, 0, -1, 0);
cullBack = normal.Noralized.Dot(E) < 0 ? true : false;//法向量与 视向量的点积小于0 则剔除
}
public Triangle3D(vector4 a, vector4 b, vector4 c)
{
this.A = this.a = new vector4(a);
this.B = this.b = new vector4(b);
this.C = this.c = new vector4(c);
}
/// <summary>
/// 向量点积得到 夹角
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public float Dot(vector4 v)
{
return((float)(this.x * v.x + this.y * v.y + this.z * v.z));
}
/// <summary>
/// 向量叉乘 得到法向量
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public vector4 Cross(vector4 v)
{
return(new vector4(this.y * v.z - this.z * v.y, this.z * v.x - this.x * v.z, this.x * v.y - this.y - v.x, 0));
}
