C语言实现贝塞尔曲线无聊人士专用程序，PS钢笔工具最初原形~

Posted 2022-12-15 C语言编程俱乐部

简介

动态演示贝塞尔曲线的绘制过程。

支持任意点数、任意阶次。

点击鼠标右键，在鼠标位置将创建新的点。

按住鼠标左键拖动控制点。

空格键屏幕将清空。

一起来玩一玩吧！

运行效果

 

源码

// 程序名称：贝塞尔曲线
//
#include <math.h>				// sin
#include <stdint.h>				// uint64_t
#include <vector>				// array
#include <graphics.h>			// window

using std::vector;

#define	WIDTH			800		// 宽
#define	HEIGHT			600		// 高

struct Point  double x, y; ;

// 初始化控制点
vector<Point> controlPoints;

Point operator+(const Point& a, const Point& b)

	return Point( a.x + b.x, a.y + b.y );

Point operator*(double f, const Point& p)

	return Point(f*p.x, f*p.y);


// 计算二项式系数：C(n, k) = n! / (k!(n-k)!)
// 这里我们不用公式，使用 Pascal's Triangle
// [1],					n = 0
// [1, 1],				n = 1
// [1, 2, 1],			n = 2
// [1, 3, 3, 1],		n = 3
// [1, 4, 6, 4, 1],		n = 4
int C(int n, int k)

	vector<int> array(n + 1, 1);
	for (int i = 2; i <= n; i++)
		for (int j = i - 1; j > 0; j--)
			array[j] += array[j - 1];
	return array[k];


// 绘制贝塞尔曲线，绘制 t [0 - end_t] 范围
void drawBezier(const vector<Point>& points, double end_t)

	if (points.size() <= 1) return;
	int n = points.size() - 1; // 阶次为点数 - 1
	setfillcolor(RED);
	for (double t = 0.0; t <= end_t; t += 0.001)
	
		Point p 0 ;
		for (int k = 0; k <= n; k++)
			p = p + C(n, k) * pow(t, k) * pow(1 - t, (double)n - k) * points[k];
		// 位置四舍五入
		p.x += 0.5;
		p.y += 0.5;
		solidcircle((int)p.x, (int)p.y, 3);
	


// 递归获取每一层的控制点
void bezierLevelPoints(vector<vector<Point>>& levels, double t)

	vector<Point> &pre = levels.back();
	vector<Point> next;
	int n = pre.size();
	if (n <= 1) return;
	
	for (int i = 0; i < n - 1; i++)
	
		Point point = (1 - t) * pre[i] + t * pre[i + 1];
		next.push_back(point);
	
	levels.push_back(next);
	bezierLevelPoints(levels, t);


// 处理输入事件
void processInput()

	ExMessage msg;
	while (peekmessage(&msg, EM_MOUSE | EM_KEY))
	
		// 按住左键拖动控制点
		if (WM_MOUSEMOVE == msg.message && msg.lbutton)
		
			for (auto& p : controlPoints)
			
				int dx = (int)p.x - msg.x;
				int dy = (int)p.y - msg.y;
				if (dx * dx + dy * dy < 50)
				
					p.x = msg.x;
					p.y = msg.y;
				
			
		
		// 点击右键，创建控制点
		else if (WM_RBUTTONDOWN == msg.message && msg.rbutton)
		
			controlPoints.push_back( (double)msg.x, (double)msg.y );
		
		// 按空格键清空
		else if (WM_KEYDOWN == msg.message && msg.vkcode == VK_SPACE)
		
			controlPoints.clear();
		
	


// 画点、画线
void drawControlLines(vector<vector<Point>>& levels)
	
	int k = levels.size();
	COLORREF color[8] =  YELLOW, BROWN, CYAN, LIGHTRED, WHITE, GREEN, MAGENTA, RED ;
	for (int i = 0; i < k; i++)
	
		vector<Point> cur = levels[i];
		int n = cur.size();
		setlinecolor(color[i&0XF]);
		setfillcolor(color[i&0XF]);
		for (auto& point : cur)
			solidcircle((int)(point.x + 0.5), (int)(point.y + 0.5), 3);
		if (k <= 2) continue;
		for (int j = 0; j < n - 1; j++)
			line((int)(cur[j].x + 0.5), (int)(cur[j].y + 0.5), \\
				(int)(cur[j + 1].x + 0.5), (int)(cur[j + 1].y + 0.5));
	


int main()

	TCHAR  buf[32];
	double t = 0.f;
	double time = -1.57079632679489661923;	// pi / 2;
	double deltaTime = 0.f;					// 当前帧和上一帧的时间差
	double lastTime = 0.f;
	double currentTime = 0.f;
	uint64_t start, now, frequency;
	initgraph(WIDTH, HEIGHT);
	BeginBatchDraw();
	QueryPerformanceCounter((LARGE_INTEGER*)&start);
	QueryPerformanceFrequency((LARGE_INTEGER*)&frequency);
	while (1)
	
		cleardevice();
		QueryPerformanceCounter((LARGE_INTEGER*)&now);
		currentTime = (double)(now - start) / frequency;
		deltaTime = currentTime - lastTime;
		lastTime = currentTime;

		// 保证不同帧率下绘制速度一致
		time += 1.5 * deltaTime;
		t = 0.5 * (1 + sin(time));
		
		// 根据鼠标拖动更新控制点
		processInput();
		// 得到每一层的控制点
		vector<vector<Point>> levels( controlPoints );
		bezierLevelPoints(levels, t);
		// 绘制控制点、控制线
		drawControlLines(levels);
		// 绘制 0 - t 范围内的贝塞尔曲线
		drawBezier(controlPoints, t);

		// 提示信息
		outtextxy(0,  0, L" Right Mouse Button to Create Points.");
		outtextxy(0, 16, L" Left  Mouse Button to Drag Points.");
		outtextxy(0, 32, L" Press SPACE to Clear.");
		swprintf_s(buf, _T(" t: %.3f"), t);
		outtextxy(0, 48, buf);
		swprintf_s(buf, _T(" time: %.0fms"), 1000 * deltaTime);
		outtextxy(0, 64, buf);
		swprintf_s(buf, _T(" fps: %d"), (int)(1.f / deltaTime));
		outtextxy(0, 80, buf);
		FlushBatchDraw();
	
	return 0;

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