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
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:joy:
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。。
#include <windows.h>
// g a.cpp -o a.exe -lgdi32 && a.exe
void 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;
}
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。
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 = 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。
def 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
# 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。
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] = 1
for 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maps
def 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 =1
scan_fill()
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：
import time
import win32gui
dc = 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] = 1
for 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maps
def 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 =1
scan_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，
import win32gui
import math
import pygame
dc = 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 = sy
def 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 True
def 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 None
def 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 True
def 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 = 60
h = 100
def 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 res
polygon_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
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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