151 lines
4.8 KiB
Python
151 lines
4.8 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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from mpl_toolkits.mplot3d import Axes3D
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def homo2cart(points):
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'''将齐次坐标转换为笛卡尔坐标'''
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points=points[:,:-1]/points[:,-1:]
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return points
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def projection_trans(view_point,points):
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'''获得投影变换之后的点阵'''
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x0,y0,z0 = view_point[0],view_point[1],view_point[2]
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d=-1*z0
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mtx=np.array([[1,0,0,0],
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[0,1,0,0],
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[x0/d,y0/d,0,1/d],
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[0,0,0,1]],dtype=np.float32)
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print(mtx)
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new_points=np.matmul(points,mtx)
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return new_points
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def one_point_perspective(L,M,N,view_point,point):
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'''一点透视：移动L，M，N'''
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mtx_mv=np.array([[1,0,0,0],
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[0,1,0,0],
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[0,0,1,0],
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[L,M,N,1]],dtype=np.float32)
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new_point=np.matmul(point,mtx_mv)
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return new_point
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def two_point_perspective(L,M,N,a,view_point,point):
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'''二点透视'''
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#先移动L，M，N
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mtx_mv=np.array([[1,0,0,0],
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[0,1,0,0],
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[0,0,1,0],
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[L,M,N,1]],dtype=np.float32)
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point=np.matmul(point,mtx_mv)
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#绕y轴旋转 a 度（a<90deg）
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a=a/180*np.pi
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mtx_roty=np.array([[np.cos(a),0,np.sin(a),0],
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[0,1,0,0],
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[-1*np.sin(a),0,np.cos(a),0],
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[0,0,0,1]],dtype=np.float32)
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new_point=np.matmul(point,mtx_roty)
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return new_point
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def three_point_perspective(L,M,N,a,b,view_point,point):
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'''三点透视'''
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#先移动L，M，N
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mtx_mv=np.array([[1,0,0,0],
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[0,1,0,0],
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[0,0,1,0],
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[L,M,N,1]],dtype=np.float32)
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point=np.matmul(point,mtx_mv)
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#绕y轴旋转 a 度（a<90deg）
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a=a/180*np.pi
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mtx_roty=np.array([[np.cos(a),0,np.sin(a),0],
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[0,1,0,0],
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[-1*np.sin(a),0,np.cos(a),0],
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[0,0,0,1]],dtype=np.float32)
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point=np.matmul(point,mtx_roty)
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#绕x轴旋转 b 度（b<90deg）
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b=b/180*np.pi
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mtx_rotx=np.array([[1,0,0,0],
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[0,np.cos(b),np.sin(b),0],
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[0,-1*np.sin(b),np.cos(b),0],
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[0,0,0,1]],dtype=np.float32)
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new_point=np.matmul(point,mtx_rotx)
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return new_point
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def draw(view_point,ori_points,mv_points,new_points):
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plt.scatter(new_points[:,0],new_points[:,1],c="black")
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plt.plot(new_points[:,0],new_points[:,1],c="black")
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ax=Axes3D(plt.figure())
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x = np.linspace(-6,6,100)
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y = np.linspace(-6,6,100)
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X, Y = np.meshgrid(x, y)
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ax.plot_surface(X,Y,Z=X*0,color='g',alpha=0.3)
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#原来的点阵
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ax.scatter(ori_points[:,0],ori_points[:,1],ori_points[:,2],c="brown")
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ax.plot(ori_points[:,0],ori_points[:,1],ori_points[:,2],c="brown")
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#透视移动后
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ax.scatter(mv_points[:,0],mv_points[:,1],mv_points[:,2])
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ax.scatter(view_point[0],view_point[1],view_point[2],c='r')
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ax.plot(mv_points[:,0],mv_points[:,1],mv_points[:,2])
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ax.get_proj = lambda: np.dot(Axes3D.get_proj(ax), np.diag([1,1, 1, 1]))
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#投影后
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ax.scatter(new_points[:,0],new_points[:,1],c="black")
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ax.plot(new_points[:,0],new_points[:,1],c="black")
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#原来与移动后点两两连接
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for i in range(len(mv_points)):
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ax.plot([ori_points[i,0],mv_points[i,0]],[ori_points[i,1],mv_points[i,1]],[ori_points[i,2],mv_points[i,2]],c="pink",linestyle='--')
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#两组点两两连接
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for i in range(len(mv_points)):
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ax.plot([mv_points[i,0],view_point[0]],[mv_points[i,1],view_point[1]],[mv_points[i,2],view_point[2]],c='y',linestyle='dashdot')
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ax.set_zlabel('Z', fontdict={'size': 15, 'color': 'red'})
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ax.set_ylabel('Y', fontdict={'size': 15, 'color': 'red'})
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ax.set_xlabel('X', fontdict={'size': 15, 'color': 'red'})
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plt.show()
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#视点（0，0，-1，1）
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view_point = np.array([4,4,-2,1],dtype=np.float32)
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#以（0，0，0）为原点的正方体
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points= np.array([[0,0,0,1],
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[2,0,0,1],
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[2,2,0,1],
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[0,2,0,1],
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[0,0,0,1],
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[0,0,2,1],
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[2,0,2,1],
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[2,2,2,1],
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[0,2,2,1],
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[0,0,2,1],
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[0,0,0,1],
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[2,0,0,1],
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[2,0,2,1],
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[2,2,2,1],
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[2,2,0,1],
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[0,2,0,1],
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[0,2,2,1]],dtype=np.float32)
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#获得透视移动后的点和投影后的点
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#per_points=one_point_perspective(6,5,1,view_point,points)
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#per_points=two_point_perspective(3,3,2,60,view_point,points)
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#透视移动后的点
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per_points=three_point_perspective(3,3,2,60,60,view_point,points)
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#投影后的点
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pro_points=projection_trans(view_point,per_points)
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#转为笛卡尔坐标系
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per_points=homo2cart(per_points)
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pro_points=homo2cart(pro_points)
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#画图
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draw(view_point,points,per_points,pro_points) |