用鼠标左键确定四个控制点,画出控制线,然后鼠标右键分别绘制三次Bezier曲线和三次B样条曲线
时间: 2023-06-19 20:07:15 浏览: 121
很抱歉,我作为一个文字AI助手,无法提供绘制图形的功能。但是我可以告诉你如何使用Python中的turtle库来绘制Bezier曲线和B样条曲线。
首先,我们需要导入turtle库:
```python
import turtle
```
接下来,我们需要定义四个控制点:
```python
control_points = [(-100, 50), (-50, 200), (50, -200), (100, 50)]
```
然后,我们可以使用turtle库中的goto函数来绘制控制线:
```python
turtle.penup()
turtle.goto(control_points[0])
turtle.pendown()
for point in control_points[1:]:
turtle.goto(point)
```
接下来,我们可以使用Python中的Bezier曲线算法来计算Bezier曲线上的点。这里我们使用一个名为de_casteljau的函数来实现:
```python
def de_casteljau(points, t):
if len(points) == 1:
return points[0]
new_points = []
for i in range(len(points)-1):
x = (1-t)*points[i][0] + t*points[i+1][0]
y = (1-t)*points[i][1] + t*points[i+1][1]
new_points.append((x, y))
return de_casteljau(new_points, t)
```
最后,我们可以使用turtle库中的goto函数来绘制Bezier曲线:
```python
turtle.penup()
turtle.goto(control_points[0])
turtle.pendown()
for t in range(101):
point = de_casteljau(control_points, t/100)
turtle.goto(point)
```
要绘制B样条曲线,我们需要使用Python中的B样条算法来计算B样条曲线上的点。这里我们使用一个名为bspline的函数来实现:
```python
def bspline(points, degree=3, periodic=False):
if periodic:
points = points + points[:degree+1]
else:
points = [(2*points[0][0]-points[degree][0], 2*points[0][1]-points[degree][1])] * degree + points
points = points + [2*points[-1]-points[-degree-2]] * degree
knots = range(len(points)+degree-1)
return [de_boor(knots, points, degree, t) for t in range(degree-1, len(points)-degree+2)]
```
然后,我们可以使用turtle库中的goto函数来绘制B样条曲线:
```python
turtle.penup()
turtle.goto(points[0])
turtle.pendown()
for point in bspline(points):
turtle.goto(point)
```
完整代码如下:
```python
import turtle
def de_casteljau(points, t):
if len(points) == 1:
return points[0]
new_points = []
for i in range(len(points)-1):
x = (1-t)*points[i][0] + t*points[i+1][0]
y = (1-t)*points[i][1] + t*points[i+1][1]
new_points.append((x, y))
return de_casteljau(new_points, t)
def bspline(points, degree=3, periodic=False):
if periodic:
points = points + points[:degree+1]
else:
points = [(2*points[0][0]-points[degree][0], 2*points[0][1]-points[degree][1])] * degree + points
points = points + [2*points[-1]-points[-degree-2]] * degree
knots = range(len(points)+degree-1)
return [de_boor(knots, points, degree, t) for t in range(degree-1, len(points)-degree+2)]
def de_boor(knots, points, degree, t):
if degree == 0:
return points[0]
i = bisect.bisect(knots, t) - 1
alpha = (t-knots[i]) / (knots[i+degree]-knots[i])
return ((1-alpha)*de_boor(knots, points, degree-1, t) + alpha*de_boor(knots, points, degree-1, t))
control_points = [(-100, 50), (-50, 200), (50, -200), (100, 50)]
turtle.speed(0)
turtle.penup()
turtle.goto(control_points[0])
turtle.pendown()
for point in control_points[1:]:
turtle.goto(point)
turtle.penup()
turtle.goto(control_points[0])
turtle.pendown()
for t in range(101):
point = de_casteljau(control_points, t/100)
turtle.goto(point)
turtle.penup()
turtle.goto(control_points[0])
turtle.pendown()
for point in bspline(control_points):
turtle.goto(point)
turtle.done()
```
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