用python写一份ARAP代码
时间: 2023-05-17 08:05:06 浏览: 115
当然可以,ARAP(As-Rigid-As-Possible)是一种形变技术,可以用于三维模型的形变和动画。以下是一个简单的 Python 实现:
```python
import numpy as np
from scipy.sparse import lil_matrix
from scipy.sparse.linalg import spsolve
def arap(vertices, faces, iterations=10, weight=1.0):
# 计算每个顶点的邻居
neighbors = [[] for i in range(len(vertices))]
for face in faces:
for i in range(3):
neighbors[face[i]].append(face[(i+1)%3])
neighbors[face[i]].append(face[(i+2)%3])
for i in range(len(vertices)):
neighbors[i] = list(set(neighbors[i]))
# 初始化每个顶点的权重矩阵
weights = [lil_matrix((3, 3)) for i in range(len(vertices))]
for i in range(len(vertices)):
for j in neighbors[i]:
vij = vertices[j] - vertices[i]
weights[i] += np.outer(vij, vij)
weights[i] = weight * np.linalg.inv(weights[i])
# 迭代优化每个顶点的位置
for it in range(iterations):
for i in range(len(vertices)):
b = np.zeros(3)
for j in neighbors[i]:
vij = vertices[j] - vertices[i]
b += weights[i].dot(vij)
vertices[i] = spsolve(weights[i], b)
return vertices
```
这个代码实现了一个简单的 ARAP 算法,输入参数为顶点坐标和三角形面片,输出为优化后的顶点坐标。算法的核心是计算每个顶点的权重矩阵,然后迭代优化每个顶点的位置。