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本文目录一览：
1、pos机器动图
pos机器动图
最近读研期间上了计算机可视化的课，老师也对计算机图形学的实现布置了相关的作业。虽然我没有系统地学过图形可视化的课，但是我之前逆向过一些游戏引擎，除了保护驱动之外，因为要做透视，接触过一些计算机图形学的基础常识。这次的作业主要分为2个主要模块，一个是实现画线，画圆的算法，还有填充的算法，以及裁剪的算法。之前工作的时候虽然参与过一些数据可视化大屏的设计，但是当时主要的工作使用Echarts或者G2做业务组件开发，并没有对画线，填充，裁剪等基础算法做过实现。这次就着这个机会我就想了解一些。实现的效果如下(动图加载可能有些慢)：
扫描线填充过程#裁剪过程（根据鼠标位置，实时裁剪多边形，右边的蓝色是裁剪后的图形）#为什么选择win32 api画图#选择win32的原因是我想做一些与众不同的实现方法，比起用D3或者Echarts这种webGL的实现方式，我更想直接在显示器上画出图像，看起来更极客一些。这也导致了录屏软件没办法捕捉，只能用手机来录制
为什么不选C++而选择python#主要是python能对内存做个管理，C++直接调这种底层的接口会把内存搞坏掉，导致电脑变得特别卡。。不信大家可以在电脑上编译运行这段代码2分钟试一试，如果你电脑没炸，算你有钱。。
Copy#include <windows.h>// g++ a.cpp -o a.exe -lgdi32 && a.exevoid bresenham(int x0,int y0,int x1,int y1){ int dx = abs(x1-x0); int dy = abs(y1-y0); int sx = x0<x1 ? 1 : -1; int sy = y0<y1 ? 1 : -1; int err = dx-dy; int e2; while(1){ SetPixel(GetDC(0),x0,y0,RGB(255,0,0)); if(x0==x1 && y0==y1) break; e2 = 2*err; if(e2>-dy){ err = err-dy; x0 = x0+sx; } if(e2<dx){ err = err+dx; y0 = y0+sy; } }}void draw_polygon(int x[], int y[], int n){ int i; for (i = 0; i < n - 1; i++) bresenham(x[i], y[i], x[i + 1], y[i + 1]); bresenham(x[n - 1], y[n - 1], x[0], y[0]);}int main(){ HDC hdc = GetDC(0); int x[4] = {100,200,300,100}; int y[4] = {100,100,200,200}; while (1) { draw_polygon(x,y,4); ReleaseDC(0, hdc); } return 0;}画线#
对于画线部分，我这里使用了一个叫bresenham算法。。虽然我念不出名字，但是这个算法能够帮助我们实现画线运算，还有后面的中心圆填充，多边形绘画等方法。而且不通过浮点数的运算，直接变成整数运算，算法实现的函数如下所示，看起来比较简单，运行速度也很快。
Copydef bresenham(x0, y0, x1, y1 , color): dx = abs(x1 - x0) dy = abs(y1 - y0) sx = 1 if x0 < x1 else -1 sy = 1 if y0 < y1 else -1 err = dx - dy while True: win32gui.SetPixel(dc, x0, y0, color) if x0 == x1 and y0 == y1: break e2 = 2 * err if e2 > -dy: err -= dy x0 += sx if e2 < dx: err += dx y0 += sy
我的屏幕分辨率是1920x1080的，只要在电脑里调用这个函数，把两个点的坐标填进去，就可以在显示器屏幕上画一条线。
中心圆算法#这个中心圆算法相对来说就比画线的算法在理解上面难很多，但是实现起来更简单一些，分成8个关于直线的和坐标轴对称的区域画圆，因此知道一个就可以画出其他几个，下面是实现过程。
Copydef draw_circle(x, y, r): x0 = 0 y0 = r d = 3 - 2 * r while x0 <= y0: win32gui.SetPixel(dc, x + x0, y + y0, 0xffffff) win32gui.SetPixel(dc, x + y0, y + x0, 0xffffff) win32gui.SetPixel(dc, x - y0, y + x0, 0xffffff) win32gui.SetPixel(dc, x - x0, y + y0, 0xffffff) win32gui.SetPixel(dc, x - x0, y - y0, 0xffffff) win32gui.SetPixel(dc, x - y0, y - x0, 0xffffff) win32gui.SetPixel(dc, x + y0, y - x0, 0xffffff) win32gui.SetPixel(dc, x + x0, y - y0, 0xffffff) if d < 0: d += 4 * x0 + 6 else: d += 4 * (x0 - y0) + 10 y0 -= 1 x0 += 1
在中心圆填充这里，可以取个巧，把几个顶点直接用画线的算法一行一行填充上去。就可以实现下面的效果。代码如下
Copy# 画实心圆def draw_circle_fill(x0, y0, r): x = 0 y = r d = 3 - 2 * r while x <= y: time.sleep(0.01) bresenham(x0 + x, y0 + y, x0 - x, y0 + y) time.sleep(0.01) bresenham(x0 + x, y0 - y, x0 - x, y0 - y) time.sleep(0.01) bresenham(x0 + y, y0 + x, x0 - y, y0 + x) time.sleep(0.01) bresenham(x0 + y, y0 - x, x0 - y, y0 - x) if d < 0: d += 4 * x + 6 else: d += 4 * (x - y) + 10 y -= 1 x += 1扫描线填充#
扫描线填充的算法就比较难实现了，需要找到起始的种子，还有每行的种子，因为我这里仅仅用顶点实现起来过于复杂，就索性偷懒用了数组。下面的算法实现部分仅供参考，具体的实现包括种子的选择等等，可以更好一些。
Copymaps = [[0 for x in range(0,400)] for x in range(0,400)]for i in range(200,300): maps[i][200] = 1 maps[200][i] = 1 maps[i][300] = 1 maps[300][i] = 1for i in range(230,270): maps[i][230] = 1 maps[i][270] = 1 maps[230][i] = 1 maps[270][i] = 1# 扫描填充mapsdef scan_fill(): seed = (271,296) stack = [] stack.append(seed) while len(stack) > 0: (x,y) = stack.pop() # 如果已经被填充过，则跳过 if(maps[x][y] == 1): continue # 横向填充并记录lx rx i=0 time.sleep(0.01) while(maps[x+i][y] == 0): maps[x+i][y] = 1 win32gui.SetPixel(dc, x+i, y, 0xffffff) i += 1 rx = x+i-1 i=1 while(maps[x-i][y] == 0): maps[x-i][y] = 1 win32gui.SetPixel(dc, x-i, y, 0xffffff) i+=1 lx = x-i+1 # 下一个种子 if y+1>=300: continue i=0 while(maps[lx+i][y+1] == 0): if(maps[lx+i+1][y+1]==1): stack.append((lx+i,y+1)) break i+=1 i=0 while(maps[rx-i][y+1] == 0): if(maps[rx-i-1][y+1]==1): stack.append((rx-i,y+1)) break i+=1 if y-1<=0: continue i=0 while(maps[lx+i][y-1] == 0): if(maps[lx+i+1][y-1]==1): stack.append((lx+i,y-1)) break i+=1 i=0 while(maps[rx-i][y-1] == 0): if(maps[rx-i-1][y-1]==1): stack.append((rx-i,y-1)) break i+=1scan_fill()这里是所有代码#
上面的代码都是剪切过的，完整的代码如下所示，运行后大家就可以在显示器上看到运行过程：
Copyimport timeimport win32guidc = win32gui.GetDC(0)maps = [[0 for x in range(0,400)] for x in range(0,400)]for i in range(200,300): maps[i][200] = 1 maps[200][i] = 1 maps[i][300] = 1 maps[300][i] = 1for i in range(230,270): maps[i][230] = 1 maps[i][270] = 1 maps[230][i] = 1 maps[270][i] = 1# 中点算法画圆def draw_circle(x, y, r): x0 = 0 y0 = r d = 3 - 2 * r while x0 <= y0: time.sleep(0.01) win32gui.SetPixel(dc, x + x0, y + y0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x + y0, y + x0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x - y0, y + x0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x - x0, y + y0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x - x0, y - y0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x - y0, y - x0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x + y0, y - x0, 0xffffff) time.sleep(0.01) win32gui.SetPixel(dc, x + x0, y - y0, 0xffffff) if d < 0: d += 4 * x0 + 6 else: d += 4 * (x0 - y0) + 10 y0 -= 1 x0 += 1# 画线def bresenham(x0, y0, x1, y1): dx = abs(x1 - x0) dy = abs(y1 - y0) sx = 1 if x0 < x1 else -1 sy = 1 if y0 < y1 else -1 err = dx - dy while True: #time.sleep(0.01) win32gui.SetPixel(dc, x0, y0, 0xffffff) if x0 == x1 and y0 == y1: break e2 = 2 * err if e2 > -dy: err -= dy x0 += sx if e2 < dx: err += dx y0 += sy# 画实心圆def draw_circle_fill(x0, y0, r): x = 0 y = r d = 3 - 2 * r while x <= y: time.sleep(0.01) bresenham(x0 + x, y0 + y, x0 - x, y0 + y) time.sleep(0.01) bresenham(x0 + x, y0 - y, x0 - x, y0 - y) time.sleep(0.01) bresenham(x0 + y, y0 + x, x0 - y, y0 + x) time.sleep(0.01) bresenham(x0 + y, y0 - x, x0 - y, y0 - x) if d < 0: d += 4 * x + 6 else: d += 4 * (x - y) + 10 y -= 1 x += 1# 画多边形def draw_polygon(points): for i in range(len(points)): x0 = points[i][0] y0 = points[i][1] x1 = points[(i + 1) % len(points)][0] y1 = points[(i + 1) % len(points)][1] bresenham(x0, y0, x1, y1)# 画椭圆def draw_ellipse(x0, y0, a, b): x = 0 y = b a2 = a * a b2 = b * b d = b2 - a2 * b + a2 / 4 while b2 * x <= a2 * y: win32gui.SetPixel(dc, x0 + x, y0 + y, 0xffffff) win32gui.SetPixel(dc, x0 - x, y0 + y, 0xffffff) win32gui.SetPixel(dc, x0 + x, y0 - y, 0xffffff) win32gui.SetPixel(dc, x0 - x, y0 - y, 0xffffff) if d < 0: d += b2 * (2 * x + 3) else: d += b2 * (2 * x - 2 * y + 5) y -= 1 x += 1 d1 = b2 * (x + 0.5) * (x + 0.5) + a2 * (y - 1) * (y - 1) - a2 * b2 while y >= 0: win32gui.SetPixel(dc, x0 + x, y0 + y, 0xffffff) win32gui.SetPixel(dc, x0 - x, y0 + y, 0xffffff) win32gui.SetPixel(dc, x0 + x, y0 - y, 0xffffff) win32gui.SetPixel(dc, x0 - x, y0 - y, 0xffffff) if d1 > 0: d1 -= a2 * (2 * y - 1) d1 += b2 * (2 * x + 3) x += 1 y -= 1# 画矩形def draw_rectangle(x0, y0, x1, y1): bresenham(x0, y0, x1, y0) bresenham(x1, y0, x1, y1) bresenham(x1, y1, x0, y1) bresenham(x0, y1, x0, y0)# 扫描填充mapsdef scan_fill(): seed = (271,296) stack = [] stack.append(seed) while len(stack) > 0: (x,y) = stack.pop() # 如果已经被填充过，则跳过 if(maps[x][y] == 1): continue # 横向填充并记录lx rx i=0 time.sleep(0.01) while(maps[x+i][y] == 0): maps[x+i][y] = 1 win32gui.SetPixel(dc, x+i, y, 0xffffff) i += 1 rx = x+i-1 i=1 while(maps[x-i][y] == 0): maps[x-i][y] = 1 win32gui.SetPixel(dc, x-i, y, 0xffffff) i+=1 lx = x-i+1 # 下一个种子 if y+1>=300: continue i=0 while(maps[lx+i][y+1] == 0): if(maps[lx+i+1][y+1]==1): stack.append((lx+i,y+1)) break i+=1 i=0 while(maps[rx-i][y+1] == 0): if(maps[rx-i-1][y+1]==1): stack.append((rx-i,y+1)) break i+=1 if y-1<=0: continue i=0 while(maps[lx+i][y-1] == 0): if(maps[lx+i+1][y-1]==1): stack.append((lx+i,y-1)) break i+=1 i=0 while(maps[rx-i][y-1] == 0): if(maps[rx-i-1][y-1]==1): stack.append((rx-i,y-1)) break i+=1scan_fill()while True: # 画线 bresenham(400, 900, 1000, 700) # 填充圆 draw_circle_fill(900, 500, 100) # 中心圆 draw_circle(1000, 200, 100) # 椭圆 draw_ellipse(1500, 200, 100, 100) # 矩形 draw_rectangle(1100, 400, 1200, 500) # 多边形 draw_polygon([(900, 1000), (800, 800), (1000, 900), (1100, 1000)]) #三角形 draw_polygon([(400, 200), (500, 300), (600, 200)])裁剪#
裁剪这里简直就是我的噩梦，因为我之前为了极客选择了仅仅知道顶点就画出裁剪过的多边形，导致我没有数组，只能设计更极客的算法。最后我找到了一种裁剪凸多边形的办法，大致就是找到每个线段的交点，然后顺时针方向对交点和在主多边形，副多边形的顶点排序，最后就可以实现裁剪。代码超级复杂，
Copyimport win32guiimport mathimport pygamedc = win32gui.GetDC(0)# 获取鼠标的位置mouse_x=win32gui.GetCursorPos()[0]mouse_y=win32gui.GetCursorPos()[1]temp = win32gui.GetCursorPos()def get_mouse_pos(): global mouse_x, mouse_y mouse_x = win32gui.GetCursorPos()[0] mouse_y = win32gui.GetCursorPos()[1]clock = pygame.time.Clock()temp2 = []def bresenham(x0, y0, x1, y1 , color): dx = abs(x1 - x0) dy = abs(y1 - y0) sx = 1 if x0 < x1 else -1 sy = 1 if y0 < y1 else -1 err = dx - dy while True: win32gui.SetPixel(dc, x0, y0, color) if x0 == x1 and y0 == y1: break e2 = 2 * err if e2 > -dy: err -= dy x0 += sx if e2 < dx: err += dx y0 += sydef draw_rectangle(x0, y0, x1, y1): bresenham(x0, y0, x1, y0,0xffffff) bresenham(x1, y0, x1, y1,0xffffff) bresenham(x1, y1, x0, y1,0xffffff) bresenham(x0, y1, x0, y0,0xffffff)def draw_polygon(points): for i in range(len(points)): x0 = points[i][0] y0 = points[i][1] x1 = points[(i + 1) % len(points)][0] y1 = points[(i + 1) % len(points)][1] bresenham(x0, y0, x1, y1,0x00ff00)def draw_polygon_black(points): for i in range(len(points)): x0 = points[i][0] y0 = points[i][1] x1 = points[(i + 1) % len(points)][0] y1 = points[(i + 1) % len(points)][1] bresenham(x0, y0, x1, y1,0x000000)# 线段是否相交def IsRectCross(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y): return min(p1x,p2x) <= max(q1x,q2x) and min(q1x,q2x) <= max(p1x,p2x) and min(p1y,p2y) <= max(q1y,q2y) and min(q1y,q2y) <= max(p1y,p2y)def IsLineSegmentCross(pFirst1x,pFirst1y,pFirst2x,pFirst2y,pSecond1x,pSecond1y,pSecond2x,pSecond2y): line1 = pFirst1x * (pSecond1y - pFirst2y) + pFirst2x * (pFirst1y - pSecond1y) + pSecond1x * (pFirst2y - pFirst1y) line2 = pFirst1x * (pSecond2y - pFirst2y) + pFirst2x * (pFirst1y - pSecond2y) + pSecond2x * (pFirst2y - pFirst1y) if (((line1 ^ line2) >= 0) and not (line1 == 0 and line2 == 0)): return False line1 = pSecond1x * (pFirst1y - pSecond2y) + pSecond2x * (pSecond1y - pFirst1y) + pFirst1x * (pSecond2y - pSecond1y) line2 = pSecond1x * (pFirst2y - pSecond2y) + pSecond2x * (pSecond1y - pFirst2y) + pFirst2x * (pSecond2y - pSecond1y) if (((line1 ^ line2) >= 0) and not (line1 == 0 and line2 == 0)): return False return Truedef GetCrossPoint(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y): if(IsRectCross(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y)): if (IsLineSegmentCross(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y)): tmpLeft = (q2x - q1x) * (p1y - p2y) - (p2x - p1x) * (q1y - q2y) tmpRight = (p1y - q1y) * (p2x - p1x) * (q2x - q1x) + q1x * (q2y - q1y) * (p2x - p1x) - p1x * (p2y - p1y) * (q2x - q1x) if (tmpLeft == 0): return None x = (int)(tmpRight/tmpLeft) tmpLeft = (p1x - p2x) * (q2y - q1y) - (p2y - p1y) * (q1x - q2x) tmpRight = p2y * (p1x - p2x) * (q2y - q1y) + (q2x- p2x) * (q2y - q1y) * (p1y - p2y) - q2y * (q1x - q2x) * (p2y - p1y) if (tmpLeft == 0): return None y = (int)(tmpRight/tmpLeft) return (x,y) else: return None else: return Nonedef draw_rectangle_black(x0, y0, x1, y1): bresenham(x0, y0, x1, y0,0x000000) bresenham(x1, y0, x1, y1,0x000000) bresenham(x1, y1, x0, y1,0x000000) bresenham(x0, y1, x0, y0,0x000000)# 判断点是否在多边形内def IsPointInPolygon(points, x, y): nCross = 0 for i in range(len(points)): p1x = points[i][0] p1y = points[i][1] p2x = points[(i + 1) % len(points)][0] p2y = points[(i + 1) % len(points)][1] if (y > min(p1y, p2y)): if (y <= max(p1y, p2y)): if (x <= max(p1x, p2x)): if (p1y != p2y): xinters = (y - p1y) * (p2x - p1x) / (p2y - p1y) + p1x if (p1x == p2x or x <= xinters): nCross += 1 if (nCross % 2 == 0): return False else: return Truedef getNonRepeatList(data): new_data = [] for i in range(len(data)): if data[i] not in new_data: new_data.append(data[i]) return new_data# 判断两多边形重叠部分 返回一个多边形def IsPolygonCross(points1, points2): result = [] for i in range(len(points1)): p1x = points1[i][0] p1y = points1[i][1] p2x = points1[(i + 1) % len(points1)][0] p2y = points1[(i + 1) % len(points1)][1] for j in range(len(points2)): q1x = points2[j][0] q1y = points2[j][1] q2x = points2[(j + 1) % len(points2)][0] q2y = points2[(j + 1) % len(points2)][1] if (IsPointInPolygon(points1, q1x, q1y) and (q1x, q1y) not in result): result.append((q1x, q1y)) if (IsPointInPolygon(points1, q2x, q2y) and (q2x, q2y) not in result): result.append((q2x, q2y)) if (IsPointInPolygon(points2, p1x, p1y) and (p1x, p1y) not in result): result.append((p1x, p1y)) if (IsPointInPolygon(points2, p2x, p2y) and (p2x, p2y) not in result): result.append((p2x, p2y)) if (IsRectCross(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y)): if GetCrossPoint(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y) != None: (x, y) = GetCrossPoint(p1x, p1y, p2x, p2y, q1x, q1y, q2x, q2y) result.append((x, y)) if (result == []): return result return (sort_points_in_clockwise_order(result))w = 60h = 100def draw_polygon_red(points): for i in range(len(points)): x0 = points[i][0] y0 = points[i][1] x1 = points[(i + 1) % len(points)][0] y1 = points[(i + 1) % len(points)][1] bresenham(x0, y0, x1, y1,0xff0000)def sort_points_in_clockwise_order(points): center = (0, 0) for point in points: center = (center[0] + point[0], center[1] + point[1]) center = (center[0] / len(points), center[1] / len(points)) points_copy = list(points) points_copy.sort(key=lambda point: math.atan2(point[0] - center[0], point[1] - center[1])) res = [] for i in points_copy: res.append((i[0]+500,i[1])) return respolygon_Points = [(600,500), (800,500), (900, 600), (900, 400),(600,300)]while True: draw_rectangle_black(temp[0],temp[1],temp[0]+w,temp[1]+h) draw_rectangle(mouse_x,mouse_y,mouse_x+w,mouse_y+h) temp = (mouse_x,mouse_y) get_mouse_pos() draw_polygon(polygon_Points) res = IsPolygonCross(polygon_Points,[(mouse_x,mouse_y),(mouse_x+w,mouse_y),(mouse_x+w,mouse_y+h),(mouse_x,mouse_y+h)]) print(res) if temp2 != []: draw_polygon_black(temp2) if res != [] and res != None: draw_polygon_red(res) temp2 = res clock.tick(120)# 60帧 总结#
计算机图形学并没有我之前想的那么好学，踩了很多坑，也补了很多知识。希望后面能再接再厉
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