public static void showMat(CMatrix4x4 mat)
{
if (isEnable)
{
for (int i = 0; i < 4; i++)
{
Console.WriteLine("[{0},{1},{2},{3}]", mat[i, 0], mat[i, 1], mat[i, 2], mat[i, 3]);
}
}
}
/// <summary>
/// 获取投影矩阵 dx风格， cvv为 x-1,1 y-1,1 z0,1
/// </summary>
/// <param name="fov">观察角，弧度</param>
/// <param name="aspect">长宽比</param>
/// <param name="zn">近裁z</param>
/// <param name="zf">远裁z</param>
/// <returns></returns>
public static CMatrix4x4 GetProjection(float fov, float aspect, float zn, float zf)
{
CMatrix4x4 p = new CMatrix4x4();
p.SetZero();
p[0, 0] = (float)(1 / (System.Math.Tan(fov * 0.5f) * aspect));
p[1, 1] = (float)(1 / System.Math.Tan(fov * 0.5f));
p[2, 2] = zf / (zf - zn);
p[2, 3] = 1f;
p[3, 2] = (zn * zf) / (zn - zf);
return p;
}
public static CMatrix4x4 GetRotateZ(float r)
{
CMatrix4x4 rm = new CMatrix4x4();
rm.Identity();
rm[0, 0] = (float)(System.Math.Cos(r));
rm[0, 1] = (float)(-System.Math.Sin(r));
//
rm[1, 0] = (float)(System.Math.Sin(r));
rm[1, 1] = (float)(System.Math.Cos(r));
return(rm);
}
/// <summary>
/// 获取投影矩阵 dx风格， cvv为 x-1,1 y-1,1 z0,1
/// </summary>
/// <param name="fov">观察角，弧度</param>
/// <param name="aspect">长宽比</param>
/// <param name="zn">近裁z</param>
/// <param name="zf">远裁z</param>
/// <returns></returns>
public static CMatrix4x4 GetProjection(float fov, float aspect, float zn, float zf)
{
CMatrix4x4 p = new CMatrix4x4();
p.SetZero();
p[0, 0] = (float)(1 / (System.Math.Tan(fov * 0.5f) * aspect));
p[1, 1] = (float)(1 / System.Math.Tan(fov * 0.5f));
p[2, 2] = zf / (zf - zn);
p[2, 3] = 1f;
p[3, 2] = (zn * zf) / (zn - zf);
return(p);
}
public static CMatrix4x4 GetRotateX(float r)
{
CMatrix4x4 rm = new CMatrix4x4();
rm.Identity();
rm[1, 1] = (float)(System.Math.Cos(r));
rm[1, 2] = (float)(-System.Math.Sin(r));
//
rm[2, 1] = (float)(System.Math.Sin(r));
rm[2, 2] = (float)(System.Math.Cos(r));
return rm;
}
/// <summary>
/// 矩阵乘法
/// </summary>
/// <param name="lhs"></param>
/// <param name="rhs"></param>
/// <returns></returns>
public static CMatrix4x4 operator *(CMatrix4x4 lhs, CMatrix4x4 rhs)
{
CMatrix4x4 nm = new CMatrix4x4();
nm.SetZero();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
for (int k = 0; k < 4; k++)
{
nm._m[i, j] += lhs._m[i,k] * rhs._m[k, j];
}
}
}
return nm;
}
/// <summary>
/// 矩阵乘法
/// </summary>
/// <param name="lhs"></param>
/// <param name="rhs"></param>
/// <returns></returns>
public static CMatrix4x4 operator *(CMatrix4x4 lhs, CMatrix4x4 rhs)
{
CMatrix4x4 nm = new CMatrix4x4();
nm.SetZero();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
for (int k = 0; k < 4; k++)
{
nm._m[i, j] += lhs._m[i, k] * rhs._m[k, j];
}
}
}
return(nm);
}
/// <summary>
/// 获取旋转矩阵
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="z"></param>
/// <param name="r"></param>
/// <returns></returns>
public static CMatrix4x4 GetRotate(float x, float y, float z, float r)
{
CMatrix4x4 rm = new CMatrix4x4();
rm.SetZero();
rm[0, 0] = (float)(x * x * (1 - System.Math.Cos(r)) + System.Math.Cos(r));
rm[0, 1] = (float)(x * y * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
rm[0, 2] = (float)(x * z * (1 - System.Math.Cos(r)) - y * System.Math.Sin(r));
//
rm[1, 0] = (float)(y * x * (1 - System.Math.Cos(r)) - z * System.Math.Sin(r));
rm[1, 1] = (float)(y * y * (1 - System.Math.Cos(r)) + System.Math.Cos(r));
rm[1, 2] = (float)(y * z * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
//
rm[2, 0] = (float)(z * x * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
rm[2, 1] = (float)(z * y * (1 - System.Math.Cos(r)) - System.Math.Sin(r));
rm[2, 2] = (float)(z * z * (1 - System.Math.Cos(r)) + z * System.Math.Cos(r));
return new CMatrix4x4();
}
/// <summary>
/// 获取旋转矩阵
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="z"></param>
/// <param name="r">弧度</param>
/// <returns></returns>
public static CMatrix4x4 GetRotate(float x, float y, float z, float r)
{
CMatrix4x4 rm = new CMatrix4x4();
rm.Identity();
rm[0, 0] = (float)(x * x * (1 - System.Math.Cos(r)) + System.Math.Cos(r));
rm[0, 1] = (float)(x * y * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
rm[0, 2] = (float)(x * z * (1 - System.Math.Cos(r)) - y * System.Math.Sin(r));
//
rm[1, 0] = (float)(y * x * (1 - System.Math.Cos(r)) - z * System.Math.Sin(r));
rm[1, 1] = (float)(y * y * (1 - System.Math.Cos(r)) + System.Math.Cos(r));
rm[1, 2] = (float)(y * z * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
//
rm[2, 0] = (float)(z * x * (1 - System.Math.Cos(r)) + z * System.Math.Sin(r));
rm[2, 1] = (float)(z * y * (1 - System.Math.Cos(r)) - System.Math.Sin(r));
rm[2, 2] = (float)(z * z * (1 - System.Math.Cos(r)) + z * System.Math.Cos(r));
return(rm);
}
/// <summary>
/// 获取视矩阵
/// </summary>
/// <param name="pos"></param>
/// <param name="lookAt"></param>
/// <param name="up"></param>
/// <returns></returns>
public static CMatrix4x4 GetView(CVector3D pos, CVector3D lookAt, CVector3D up)
{
//视线方向
CVector3D dir = lookAt - pos;
CVector3D right = CVector3D.Cross(up, dir);
right.Normalize();
//平移部分
CMatrix4x4 t = new CMatrix4x4(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
-pos.x, -pos.y, -pos.z, 1);
//旋转部分
CMatrix4x4 r = new CMatrix4x4(right.x, up.x, dir.x, 0,
right.y, up.y, dir.y, 0,
right.z, up.z, dir.z, 0,
0, 0, 0, 1);
return(t * r);
}
public static void Test()
{
CVector3D a = new CVector3D(1, 2, 1,1);
CVector3D b = new CVector3D(5, 6, 0,1);
CVector3D c = new CVector3D(1, 2, 3, 1);
float r1 = CVector3D.Dot(a,b);
CVector3D r2 = a - b;
CVector3D r3 = CVector3D.Cross(a,b);
Console.WriteLine("a dot b:{0}", r1);
Console.WriteLine("a - b:({0},{1},{2},{3})", r2.x, r2.y, r2.z, r2.w);
Console.WriteLine("a X b:({0},{1},{2},{3})", r3.x, r3.y, r3.z, r3.w);
//
CMatrix4x4 mat1 = new CMatrix4x4(1,2,3,4,
1,2,3,4,
1,2,3,4,
0,0,0,1);
CMatrix4x4 mat2 = new CMatrix4x4(1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4);
CMatrix4x4 mat3 = new CMatrix4x4();
mat3.Identity();
CMatrix4x4 mat4 = new CMatrix4x4(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
1, 2, 3, 1);
CMatrix4x4 matr1 = mat1 * mat3;
Console.WriteLine("mat1 * mat3:");
showMat(matr1);
CMatrix4x4 matr2 = mat1 * mat2;
Console.WriteLine("mat1 * mat2:");
showMat(matr2);
CVector3D r4 = a * mat1;
Console.WriteLine("a * mat1:({0},{1},{2},{3})", r4.x, r4.y, r4.z, r4.w);
CVector3D r5 = a * mat4;
Console.WriteLine("a * mat4:({0},{1},{2},{3})", r5.x, r5.y, r5.z, r5.w);
}
private void Draw(CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p)
{
DrawPanel(0, 1, 2, 3, m, v, p);
DrawPanel(4, 5, 6, 7, m, v, p);
DrawPanel(0, 4, 5, 1, m, v, p);
DrawPanel(1, 5, 6, 2, m, v, p);
DrawPanel(2, 6, 7, 3, m, v, p);
DrawPanel(3, 7, 4, 0, m, v, p);
}
/// <summary>
/// 获取视矩阵
/// </summary>
/// <param name="pos"></param>
/// <param name="lookAt"></param>
/// <param name="up"></param>
/// <returns></returns>
public static CMatrix4x4 GetView(CVector3D pos, CVector3D lookAt, CVector3D up)
{
//视线方向
CVector3D dir = lookAt - pos;
CVector3D right = CVector3D.Cross(up, dir);
right.Normalize();
//平移部分
CMatrix4x4 t = new CMatrix4x4(1,0,0,0,
0,1,0,0,
0,0,1,0,
-pos.x, -pos.y, -pos.z, 1);
//旋转部分
CMatrix4x4 r= new CMatrix4x4(right.x,up.x,dir.x,0,
right.y,up.y,dir.y,0,
right.z,up.z,dir.z,0,
0, 0, 0, 1);
return t * r;
}
/// <summary>
/// 绘制平面
/// </summary>
/// <param name="vIndex1">顶点索引</param>
/// <param name="vIndex2">顶点索引</param>
/// <param name="vIndex3">顶点索引</param>
/// <param name="vIndex4">顶点索引</param>
/// <param name="mvp">mvp矩阵</param>
private void DrawPanel(int vIndex1, int vIndex2, int vIndex3, int vIndex4, CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p)
{
CVertex p1 = new CVertex(mesh[vIndex1]);
CVertex p2 = new CVertex(mesh[vIndex2]);
CVertex p3 = new CVertex(mesh[vIndex3]);
//
DrawTriangle(p1, p2, p3, m, v, p);
p1 = new CVertex(mesh[vIndex1]);
p3 = new CVertex(mesh[vIndex3]);
CVertex p4 = new CVertex(mesh[vIndex4]);
DrawTriangle(p3, p4, p1, m, v, p);
}
/// <summary>
/// 绘制三角形
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
/// <param name="mvp"></param>
private void DrawTriangle(CVertex p1, CVertex p2, CVertex p3, CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p)
{
//--------------------几何阶段---------------------------
//变换到齐次裁剪空
SetMVPTransform(m, v, p, p1);
SetMVPTransform(m, v, p, p2);
SetMVPTransform(m, v, p, p3);
////裁剪
if (Clip(p1) == false || Clip(p2) == false || Clip(p3) == false)
{
return;
}
//背面消隐
//if (BackFaceCulling(p1, p2, p3) == false)
//{
// return;
//}
//变换到屏幕坐标
TransformToScreen(p1);
VectorMatrixTestCase.showVector3(p1.point);
TransformToScreen(p2);
VectorMatrixTestCase.showVector3(p2.point);
TransformToScreen(p3);
VectorMatrixTestCase.showVector3(p3.point);
//--------------------光栅化阶段---------------------------
//todo test
//_frameBuff.SetPixel((int)p1.point.x, (int)p1.point.y, System.Drawing.Color.White);
//_frameBuff.SetPixel((int)p2.point.x, (int)p2.point.y, System.Drawing.Color.White);
//_frameBuff.SetPixel((int)p3.point.x, (int)p3.point.y, System.Drawing.Color.White);
TriangleRasterization(p1, p2, p3);
}
private void timer1_Tick(object sender, EventArgs e)
{
lock (_frameBuff)
{
ClearBuff();
CMatrix4x4 m = new CMatrix4x4();
m.Identity();
m[3, 2] = 5;
rot += 0.1f;
m = MathUntil.GetRotateY(rot) * m;
CMatrix4x4 v = MathUntil.GetView(new CVector3D(0, 0, 0, 1), new CVector3D(0, 0, 1, 1), new CVector3D(0, 1, 0, 1));
CMatrix4x4 p = MathUntil.GetProjection((float)System.Math.PI / 4, this.MaximumSize.Width / (float)this.MaximumSize.Height, 1f, 500f);
//
Draw(m, v, p);
//
if (g1 == null)
{
g1 = this.CreateGraphics();
}
g1.Clear(System.Drawing.Color.Black);
g1.DrawImage(_frameBuff, 0, 0);
}
this.Invalidate();
}
/// <summary>
/// 进行mvp矩阵变换，将顶点变换到齐次裁剪空间
/// </summary>
private void SetMVPTransform(CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p, CVertex vertex)
{
vertex.point = vertex.point * m;
VectorMatrixTestCase.showVector3(vertex.point);
vertex.point = vertex.point * v;
VectorMatrixTestCase.showVector3(vertex.point);
vertex.point = vertex.point * p;
VectorMatrixTestCase.showVector3(vertex.point);
//得到齐次裁剪空间的点 v.point.w 中保存着原来的z(具体是z还是-z要看使用的投影矩阵,我们使用投影矩阵是让w中保存着z)
//onePerZ 保存1/z，方便之后对1/z关于x’、y’插值得到1/z’
vertex.onePerZ = 1 / vertex.point.w;
//校正的推论： s/z、t/z和x’、y’也是线性关系。而我们之前知道1/z和x’、y’是线性关系。则我们得出新的思路：对1/z关于x’、y’插值得到1/z’，然后对s/z、t/z关于x’、y’进行插值得到s’/z’、t’/z’，然后用s’/z’和t’/z’分别除以1/z’，就得到了插值s’和t’
//这里将需要插值的信息都乘以1/z 得到 s/z和t/z等，方便光栅化阶段进行插值
vertex.u *= vertex.onePerZ;
vertex.v *= vertex.onePerZ;
//
vertex.color.r *= vertex.onePerZ;
vertex.color.g *= vertex.onePerZ;
vertex.color.b *= vertex.onePerZ;
}
