求计算机图形：C#实现贝塞尔曲面和小球光照模型，最好有讲解
首先，了解一下贝塞尔曲面的概念和数学知识。贝塞尔曲面是通过控制点来定义的曲面，它可以用于三维几何建模、计算机图形学中的曲面绘制等领域。在计算机图形学中，我们可以用贝塞尔曲面来模拟三维物体的形态，并使用小球光照模型来实现光照效果。
接下来，我们来看看如何用C#实现这个程序：
struct Point3D
{
public double X;
public double Y;
public double Z;
public Color Color;
};
private Point3D[,,] grid = new Point3D[4, 4, 4];
private void DrawBezierSurface()
{
// 计算3D网格中每个点的坐标
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
for (int k = 0; k < 4; k++)
{
double u = (double)i / 3;
double v = (double)j / 3;
double w = (double)k / 3;
double x = 0;
double y = 0;
double z = 0;
// 计算曲面上每个点的坐标
for (int p = 0; p < 4; p++)
{
for (int q = 0; q < 4; q++)
{
for (int r = 0; r < 4; r++)
{
double b_p_u = Bernstein(3, p, u);
double b_q_v = Bernstein(3, q, v);
double b_r_w = Bernstein(3, r, w);
x += grid[p, q, r].X * b_p_u * b_q_v * b_r_w;
y += grid[p, q, r].Y * b_p_u * b_q_v * b_r_w;
z += grid[p, q, r].Z * b_p_u * b_q_v * b_r_w;
}
}
}
grid[i, j, k].X = x;
grid[i, j, k].Y = y;
grid[i, j, k].Z = z;
}
}
}
// 绘制曲面
glBegin(GL_QUADS);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
for (int k = 0; k < 3; k++)
{
Point3D p1 = grid[i, j, k];
Point3D p2 = grid[i + 1, j, k];
Point3D p3 = grid[i + 1, j + 1, k];
Point3D p4 = grid[i, j + 1, k];
glColor3d(p1.Color.R / 255.0, p1.Color.G / 255.0, p1.Color.B / 255.0);
glVertex3d(p1.X, p1.Y, p1.Z);
glColor3d(p2.Color.R / 255.0, p2.Color.G / 255.0, p2.Color.B / 255.0);
glVertex3d(p2.X, p2.Y, p2.Z);
glColor3d(p3.Color.R / 255.0, p3.Color.G / 255.0, p3.Color.B / 255.0);
glVertex3d(p3.X, p3.Y, p3.Z);
glColor3d(p4.Color.R / 255.0, p4.Color.G / 255.0, p4.Color.B / 255.0);
glVertex3d(p4.X, p4.Y, p4.Z);
}
}
}
glEnd();
}
在上面的代码中，Bernstein函数用于计算伯恩斯坦多项式的值，我们需要用到这个函数来计算贝塞尔曲面上每个点的坐标。
private void DrawSphere()
{
// 计算每个顶点的法向量和反射光强度
for (int i = 0; i < numVertices; i++)
{
Point3D p = vertices[i];
Vector3 normal = Vector3.Zero;
Vector3 reflection = Vector3.Zero;
// 计算法向量
for (int j = 0; j < numTriangles; j++)
{
Triangle t = triangles[j];
if (t.P1 == p || t.P2 == p || t.P3 == p)
{
normal += t.Normal;
}
}
normal.Normalize();
// 计算反射光强度
for (int j = 0; j < numLights; j++)
{
Light l = lights[j];
Vector3 lightDir = (l.Position - p.ToVec3()).Normalized();
double diffuse = Math.Max(0, Vector3.Dot(normal, lightDir));
Vector3 viewDir = (cameraPosition.ToVec3() - p.ToVec3()).Normalized();
Vector3 reflectDir = (2 * Vector3.Dot(lightDir, normal) * normal - lightDir).Normalized();
double specular = Math.Pow(Math.Max(0, Vector3.Dot(viewDir, reflectDir)), shininess);
reflection += l.Color.ToVec3() * ((float)diffuse * diffuseCoefficient + (float)specular * specularCoefficient);
}
vertices[i].Normal = normal.ToPoint3D();
vertices[i].Reflection = reflection;
}
// 绘制每个三角形，并使用每个顶点的反射光强度来进行颜色漫反射计算
for (int i = 0; i < numTriangles; i++)
{
Triangle t = triangles[i];
Point3D p1 = vertices[t.P1].ToPoint3D();
Point3D p2 = vertices[t.P2].ToPoint3D();
Point3D p3 = vertices[t.P3].ToPoint3D();
Vector3 normal = t.Normal;
glBegin(GL_TRIANGLES);
glNormal3f(normal.X, normal.Y, normal.Z);
glColor3d(vertices[t.P1].Reflection.X, vertices[t.P1].Reflection.Y, vertices[t.P1].Reflection.Z);
glVertex3d(p1.X, p1.Y, p1.Z);
glColor3d(vertices[t.P2].Reflection.X, vertices[t.P2].Reflection.Y, vertices[t.P2].Reflection.Z);
glVertex3d(p2.X, p2.Y, p2.Z);
glColor3d(vertices[t.P3].Reflection.X, vertices[t.P3].Reflection.Y, vertices[t.P3].Reflection.Z);
glVertex3d(p3.X, p3.Y, p3.Z);
glEnd();
}
}
在上面的代码中，我们需要计算出每个顶点的法向量、反射光强度等参数，然后根据每个顶点的颜色和反射光强度来进行颜色漫反射计算。
希望以上的代码和讲解能够帮助到您。