我正在玩贝塞尔曲线试图理解它。
这是代码。
import pygame
import sys
pygame.init()
textSize = 25
font = pygame.font.Font(pygame.font.get_default_font(), textSize)
_t = 0
red = (255, 0, 0)
green = (0, 255 , 0)
blue = (0, 0 , 255)
black = (0, 0 , 0)
def drawPoint(window, p, color):
pygame.draw.circle(window, color, (p.x, p.y), p.radius)
def getPs(t):
tt = t * t
ttt = t * t * t
return(
-ttt + 3 * tt -3 * t + 1,
3 * ttt - 6 * tt + 3 * t,
-3 * ttt + 3 * tt,
ttt
)
def drawPointOnCurve(window, p, t, color, scale):
pygame.draw.circle(window, color, (5 + (t * scale), 50 + (p * scale)), 5)
def drawCurvePixel(window, p, t, color, scale):
window.set_at((5 + int(t * scale), 50 + int(p * scale)), color)
def drawVectorsAdded(window, origin, vecs):
p0End = (vecs[0][0] + origin[0], vecs[0][1] + origin[1])
p1End = (vecs[1][0] + p0End[0], vecs[1][1] + p0End[1])
p2End = (vecs[2][0] + p1End[0], vecs[2][1] + p1End[1])
p3End = (vecs[3][0] + p2End[0], vecs[3][1] + p2End[1])
pygame.draw.line(window, red, origin, p0End, 2)
pygame.draw.line(window, green, p0End, p1End, 2)
pygame.draw.line(window, blue, p1End, p2End, 2)
pygame.draw.line(window, black, p2End, p3End, 2)
class Point:
def __init__(self, origin, x, y):
self.origin = origin
self.x = x
self.y = y
self.radius = 10
self.move = False
def moveable(self, mouse, mousepos):
if mouse[0]:
rect = pygame.Rect(self.x - self.radius, self.y - self.radius, self.radius * 2, self.radius * 2)
if rect.collidepoint(mousepos):
self.move = True
if not mouse[0]:
self.move = False
if self.move:
self.x, self.y = mousepos
class Curve:
def __init__(self, origin):
self.origin = origin
self.p0 = Point(origin, origin[0] - 120, origin[1] + 30)
self.p1 = Point(origin, origin[0] + 120, origin[1] + 30)
self.p2 = Point(origin, origin[0] - 110, origin[1] - 120)
self.p3 = Point(origin, origin[0] + 110, origin[1] - 120)
def moveable(self, mouse, mousepos):
self.p0.moveable(mouse, mousepos)
self.p1.moveable(mouse, mousepos)
self.p2.moveable(mouse, mousepos)
self.p3.moveable(mouse, mousepos)
ps = (self.p0, self.p1, self.p2, self.p3)
for i in range(4):
if ps[i].move:
for j in range(4):
if i != j:
ps[j].move = False
def draw(self, window):
drawPoint(window, self.p0, red)
drawPoint(window, self.p1, green)
drawPoint(window, self.p2, blue)
drawPoint(window, self.p3, black)
pygame.draw.line(window, red, (self.p0.x, self.p0.y), (self.p1.x, self.p1.y), 3)
pygame.draw.line(window, green, (self.p1.x, self.p1.y), (self.p2.x, self.p2.y), 3)
pygame.draw.line(window, blue, (self.p2.x, self.p2.y), (self.p3.x, self.p3.y), 3)
def getControlVectors(self):
findVector = lambda p : (p.x - self.origin[0], p.y - self.origin[1])
return (findVector(self.p0), findVector(self.p1), findVector(self.p2), findVector(self.p3))
def getScaledControlVectors(self, pVals):
vectors = self.getControlVectors()
scaleVector = lambda x : (vectors[x][0] * pVals[x], vectors[x][1] * pVals[x])
return (scaleVector(0), scaleVector(1), scaleVector(2), scaleVector(3))
def getPointOnCurve(self, pVals):
vectors = self.getScaledControlVectors(pVals)
addVector = lambda v1, v2 : (v1[0] + v2[0], v1[1] + v2[1])
return addVector(self.origin, addVector(addVector(vectors[0], vectors[1]), addVector(vectors[2], vectors[3])))
def getControlPoints(self):
return (self.p0, self.p1, self.p2, self.p3)
curve = Curve((700, 500))
scale = 380
window = pygame.display.set_mode((1200, 800))
clock = pygame.time.Clock()
while True:
clock.tick(60)
events = pygame.event.get()
for event in events:
if event.type == pygame.QUIT:
pygame.quit()
sys.exit()
mouse = pygame.mouse.get_pressed()
mousePos = pygame.mouse.get_pos()
keys = pygame.key.get_pressed()
curve.moveable(mouse, mousePos)
pygame.display.set_caption(f"Bezier Curves - fps - {int(clock.get_fps())}")
if keys[pygame.K_w]: _t += 0.005
if keys[pygame.K_q]: _t -= 0.005
_t = min(1, max(_t, 0))
window.fill((255, 255, 255))
pygame.draw.rect(window, (0, 0, 0), (5, 50, 380, 380), 1)
t = 0
while t <= 1:
cp0, cp1, cp2, cp3 = getPs(t)
drawCurvePixel(window, cp0, t, red, scale)
drawCurvePixel(window, cp1, t, green, scale)
drawCurvePixel(window, cp2, t, blue, scale)
drawCurvePixel(window, cp3, t, black, scale)
pointAtTValue = curve.getPointOnCurve((cp0, cp1, cp2, cp3))
pygame.draw.circle(window, (255, 0, 255), pointAtTValue, 3)
t += 0.01
cp0, cp1, cp2, cp3 = getPs(_t)
drawPointOnCurve(window, cp0, _t, red, scale)
drawPointOnCurve(window, cp1, _t, green, scale)
drawPointOnCurve(window, cp2, _t, blue, scale)
drawPointOnCurve(window, cp3, _t, black, scale)
pygame.draw.rect(window, red, (5, 450, cp0 * 380, 50))
pygame.draw.rect(window, green, (5, 510, cp1 * 380, 50))
pygame.draw.rect(window, blue, (5, 570, cp2 * 380, 50))
pygame.draw.rect(window, black, (5, 630, cp3 * 380, 50))
curve.draw(window)
pygame.draw.circle(window, black, curve.origin, 5, 1)
pVals = (cp0, cp1, cp2, cp3)
drawVectorsAdded(window, curve.origin, curve.getScaledControlVectors(pVals))
pointAtTValue = curve.getPointOnCurve(pVals)
pygame.draw.circle(window, (255, 0, 255), pointAtTValue, 10)
val = str(_t)[0:5]
tvalue = font.render(f"t = {val}", True, black)
window.blit(tvalue, (10, 10))
pygame.display.flip()
在绘制曲线的部分
t = 0
while t <= 1:
cp0, cp1, cp2, cp3 = getPs(t)
drawCurvePixel(window, cp0, t, red, scale)
drawCurvePixel(window, cp1, t, green, scale)
drawCurvePixel(window, cp2, t, blue, scale)
drawCurvePixel(window, cp3, t, black, scale)
pointAtTValue = curve.getPointOnCurve((cp0, cp1, cp2, cp3))
pygame.draw.circle(window, (255, 0, 255), pointAtTValue, 3)
t += 0.01
如果 t 增加一个小值，它将多次重绘相同的像素，更大的值将在像素之间留下间隙。有没有办法找到一个理想的增量大小，它不会重绘像素，但也不会根据曲线留下间隙？
像素间隙：
重绘相同的像素：
