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; }