easyx图形库绘制双三次贝塞尔曲面片
时间: 2023-07-04 10:29:38 浏览: 57
以下是使用EasyX图形库绘制双三次贝塞尔曲面片的示例代码:
```
#include <graphics.h>
#include <cmath>
const int N = 4; // 控制点矩阵大小
struct Point {
int x, y;
};
Point controlPoints[N][N]; // 控制点矩阵
const int curvePointsCount = 20; // 每个方向上的曲线点数
Point curvePoints[curvePointsCount][curvePointsCount]; // 存储曲线上的点
// 计算组合数
int binomialCoeff(int n, int k) {
int res = 1;
if (k > n - k)
k = n - k;
for (int i = 0; i < k; ++i) {
res *= (n - i);
res /= (i + 1);
}
return res;
}
// 计算Bezier曲线上的点
Point bezierCurvePoint(Point* points, int n, float t) {
Point res = { 0, 0 };
for (int i = 0; i < n; i++) {
float coeff = binomialCoeff(n - 1, i) * pow(t, i) * pow(1 - t, n - 1 - i);
res.x += points[i].x * coeff;
res.y += points[i].y * coeff;
}
return res;
}
// 计算Bezier曲面上的点
Point bezierSurfacePoint(Point points[N][N], float u, float v) {
Point uCurvePoints[N], vCurvePoints[N];
for (int i = 0; i < N; i++) {
Point rowPoints[N];
for (int j = 0; j < N; j++) {
rowPoints[j] = points[i][j];
}
uCurvePoints[i] = bezierCurvePoint(rowPoints, N, u);
}
for (int i = 0; i < N; i++) {
Point colPoints[N];
for (int j = 0; j < N; j++) {
colPoints[j] = points[j][i];
}
vCurvePoints[i] = bezierCurvePoint(colPoints, N, v);
}
return bezierCurvePoint(uCurvePoints, N, v);
}
void drawBezierSurface(Point points[N][N]) {
// 计算曲面上的所有点
for (int i = 0; i < curvePointsCount; i++) {
for (int j = 0; j < curvePointsCount; j++) {
float u = i * 1.0f / (curvePointsCount - 1);
float v = j * 1.0f / (curvePointsCount - 1);
curvePoints[i][j] = bezierSurfacePoint(points, u, v);
}
}
// 绘制曲面
for (int i = 0; i < curvePointsCount - 1; i++) {
for (int j = 0; j < curvePointsCount - 1; j++) {
Point p1 = curvePoints[i][j];
Point p2 = curvePoints[i + 1][j];
Point p3 = curvePoints[i + 1][j + 1];
Point p4 = curvePoints[i][j + 1];
line(p1.x, p1.y, p2.x, p2.y);
line(p2.x, p2.y, p3.x, p3.y);
line(p3.x, p3.y, p4.x, p4.y);
line(p4.x, p4.y, p1.x, p1.y);
}
}
}
int main() {
// 初始化控制点矩阵
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
controlPoints[i][j] = { i * 100, j * 100 };
}
}
initgraph(640, 480); // 创建绘图窗口
drawBezierSurface(controlPoints); // 绘制曲面
system("pause"); // 暂停程序,等待用户关闭窗口
closegraph(); // 关闭绘图窗口
return 0;
}
```
该示例代码中,我们使用了EasyX图形库来绘制双三次贝塞尔曲面片。首先初始化了控制点矩阵,然后通过 `drawBezierSurface` 函数计算曲面上的所有点,并将这些点连接起来绘制出曲面。在 `main` 函数中,我们创建了一个640x480的绘图窗口,调用 `drawBezierSurface` 函数绘制曲面,并使用 `system("pause")` 暂停程序,等待用户关闭窗口。最后,调用 `closegraph()` 函数关闭绘图窗口。
需要注意的是,该示例代码中使用了 `line` 函数来绘制曲面上的线段,实际上这样绘制的曲面比较粗糙,可以通过使用更高级的图形库或者实现更复杂的插值算法来绘制更平滑的曲面。