最近讀研期間上了計算機可視化的課，老師也對計算機圖形學的實現布置了相關的作業。雖然我沒有系統地學過圖形可視化的課，但是我之前逆向過一些遊戲引擎，除了保護驅動之外， 因為要做透視 ，接觸過一些計算機圖形學的基礎常識。這次的作業主要分為2個主要模塊，一個是實現畫線，畫圓的算法，還有填充的算法，以及裁剪的算法。
之前工作的時候雖然參與過一些數據可視化大屏的設計，但是當時主要的工作使用Echarts或者G2做業務組件開發，并沒有對畫線，填充，裁剪等基礎算法做過實現。這次就着這個機會我就想了解一些。實現的效果如下(動圖加載可能有些慢)：
掃描線填充過程
選擇win32的原因是我想做一些與衆不同的實現方法，比起用D3或者Echarts這種webGL的實現方式，我更想直接在顯示器上畫出圖像，看起來更極客一些。這也導緻了錄屏軟件沒辦法捕捉，隻能用手機來錄制:joy:
為什麼不選C 而選擇python主要是python能對内存做個管理，C 直接調這種底層的接口會把内存搞壞掉，導緻電腦變得特别卡。。不信大家可以在電腦上編譯運行這段代碼2分鐘試一試，如果你電腦沒炸，算你有錢。。
#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;
}
對于畫線部分，我這裡使用了一個叫bresenham算法。。雖然我念不出名字，但是這個算法能夠幫助我們實現畫線運算，還有後面的中心圓填充，多邊形繪畫等方法。而且不通過浮點數的運算，直接變成整數運算，算法實現的函數如下所示，看起來比較簡單，運行速度也很快。
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，隻要在電腦裡調用這個函數，把兩個點的坐标填進去，就可以在顯示器屏幕上畫一條線。
中心圓算法這個中心圓算法相對來說就比畫線的算法在理解上面難很多，但是實現起來更簡單一些，分成8個關于直線的和坐标軸對稱的區域畫圓，因此知道一個就可以畫出其他幾個，下面是實現過程。
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
在中心圓填充這裡，可以取個巧，把幾個頂點直接用畫線的算法一行一行填充上去。就可以實現下面的效果。代碼如下
# 畫實心圓
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
掃描線填充的算法就比較難實現了，需要找到起始的種子，還有每行的種子，因為我這裡僅僅用頂點實現起來過于複雜，就索性偷懶用了數組。下面的算法實現部分僅供參考，具體的實現包括種子的選擇等等，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
# 掃描填充maps
def scan_fill():
seed = (271,296)
stack = []
stack.append(seed)
while len(stack) > 0:
(x,y) = stack.pop()
# 如果已經被填充過，則跳過
if(maps[x][y] == 1):
continue
# 橫向填充并記錄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
# 下一個種子
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()
上面的代碼都是剪切過的，完整的代碼如下所示，運行後大家就可以在顯示器上看到運行過程：
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
# 中點算法畫圓
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
# 畫線
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
# 畫實心圓
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
# 畫多邊形
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)
# 畫橢圓
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
# 畫矩形
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)
# 掃描填充maps
def scan_fill():
seed = (271,296)
stack = []
stack.append(seed)
while len(stack) > 0:
(x,y) = stack.pop()
# 如果已經被填充過，則跳過
if(maps[x][y] == 1):
continue
# 橫向填充并記錄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
# 下一個種子
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:
# 畫線
bresenham(400, 900, 1000, 700)
# 填充圓
draw_circle_fill(900, 500, 100)
# 中心圓
draw_circle(1000, 200, 100)
# 橢圓
draw_ellipse(1500, 200, 100, 100)
# 矩形
draw_rectangle(1100, 400, 1200, 500)
# 多邊形
draw_polygon([(900, 1000), (800, 800), (1000, 900), (1100, 1000)])
#三角形
draw_polygon([(400, 200), (500, 300), (600, 200)])
裁剪這裡簡直就是我的噩夢，因為我之前為了極客選擇了僅僅知道頂點就畫出裁剪過的多邊形，導緻我沒有數組，隻能設計更極客的算法。
最後我找到了一種裁剪凸多邊形的辦法，大緻就是找到每個線段的交點，然後順時針方向對交點和在主多邊形，副多邊形的頂點排序，最後就可以實現裁剪。代碼超級複雜，
import win32gui
import math
import pygame
dc = win32gui.GetDC(0)
# 獲取鼠标的位置
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)
# 線段是否相交
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)
# 判斷點是否在多邊形内
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
# 判斷兩多邊形重疊部分 返回一個多邊形
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幀
計算機圖形學并沒有我之前想的那麼好學，踩了很多坑，也補了很多知識。希望後面能再接再厲
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