Create projection.py

projection.py

@@ -0,0 +1,145 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from mpl_toolkits.mplot3d import Axes3D  
+
+def homo2cart(points):
+    '''将齐次坐标转换为笛卡尔坐标'''
+    points=points[:,:-1]/points[:,-1:]
+    return points
+
+def projection_trans(view_point,points):
+    '''获得投影变换之后的点阵'''
+    x0,y0,z0 = view_point[0],view_point[1],view_point[2]
+    d=-1*z0
+    mtx=np.array([[1,0,0,0],
+                [0,1,0,0],
+                [x0/d,y0/d,0,1/d],
+                [0,0,0,1]],dtype=np.float32)
+    print(mtx)
+    new_points=np.matmul(points,mtx)
+    return new_points
+
+def one_point_projection(L,M,N,view_point,point):
+    '''一点'''
+    mtx_mv=np.array([[1,0,0,0],
+                    [0,1,0,0],
+                    [0,0,1,0],
+                    [L,M,N,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_mv)
+   # print(point)
+    new_point=projection_trans(view_point,point)
+    return new_point,point
+
+def two_point_projection(L,M,N,a,view_point,point):
+    '''二点'''
+    #先移动L，M，N
+    mtx_mv=np.array([[1,0,0,0],
+                    [0,1,0,0],
+                    [0,0,1,0],
+                    [L,M,N,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_mv)
+
+    #绕y轴旋转 a 度（a<90deg）
+    a=a/180*np.pi
+    mtx_roty=np.array([[np.cos(a),0,np.sin(a),0],
+                    [0,1,0,0],
+                    [-1*np.sin(a),0,np.cos(a),0],
+                    [0,0,0,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_roty)
+
+   # print(point)
+    new_point=projection_trans(view_point,point)
+    return new_point,point
+
+
+def three_point_projection(L,M,N,a,b,view_point,point):
+    '''三点'''
+    #先移动L，M，N
+    mtx_mv=np.array([[1,0,0,0],
+                    [0,1,0,0],
+                    [0,0,1,0],
+                    [L,M,N,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_mv)
+    print("aaa")
+    print(point)
+    #绕y轴旋转 a 度（a<90deg）
+    a=a/180*np.pi
+    mtx_roty=np.array([[np.cos(a),0,np.sin(a),0],
+                    [0,1,0,0],
+                    [-1*np.sin(a),0,np.cos(a),0],
+                    [0,0,0,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_roty)
+    print("bbb")
+    print(point)
+    #绕x轴旋转 b 度（b<90deg）
+    b=b/180*np.pi
+    mtx_rotx=np.array([[1,0,0,0],
+                    [0,np.cos(b),np.sin(b),0],   
+                    [0,-1*np.sin(b),np.cos(b),0],
+                    [0,0,0,1]],dtype=np.float32)
+    point=np.matmul(point,mtx_rotx)
+    print("ccc")
+    print(point)
+   # print(point)
+    new_point=projection_trans(view_point,point)
+    return new_point,point
+
+
+view_point = np.array([0,0,-1,1],dtype=np.float32)
+points= np.array([[0,0,0,1],
+                [1,0,0,1],
+                [1,1,0,1],
+                [0,1,0,1],
+                [0,0,0,1],
+                [0,0,1,1],
+                [1,0,1,1],
+                [1,1,1,1],
+                [0,1,1,1],
+                [0,0,1,1],
+                [0,0,0,1],
+                [1,0,0,1],
+                [1,0,1,1],
+                [1,1,1,1],
+                [1,1,0,1],
+                [0,1,0,1],
+                [0,1,1,1]],dtype=np.float32)
+               
+
+#new_points=one_point_projection(0,0,0,view_point,points)
+new_points,ori_points=three_point_projection(2,3,1,50,30,view_point,points)
+
+new_points=homo2cart(new_points)
+
+
+def draw(view_point,ori_points,new_points):
+    plt.scatter(new_points[:,0],new_points[:,1],c="black")
+    plt.plot(new_points[:,0],new_points[:,1],c="black")
+    ax=Axes3D(plt.figure())
+
+    x = np.linspace(-6,6,100)
+    y = np.linspace(-6,6,100)
+    X, Y = np.meshgrid(x, y)
+
+
+    ax.plot_surface(X,Y,Z=X*0,color='g',alpha=0.3) 
+
+    ax.scatter(ori_points[:,0],ori_points[:,1],ori_points[:,2])
+    ax.scatter(view_point[0],view_point[1],view_point[2],c='r')
+    ax.plot(ori_points[:,0],ori_points[:,1],ori_points[:,2])
+    ax.get_proj = lambda: np.dot(Axes3D.get_proj(ax), np.diag([1,1, 0.5, 1]))
+
+    ax.scatter(new_points[:,0],new_points[:,1],c="black")
+    ax.plot(new_points[:,0],new_points[:,1],c="black")
+
+
+    ax.set_zlabel('Z', fontdict={'size': 15, 'color': 'red'})
+    ax.set_ylabel('Y', fontdict={'size': 15, 'color': 'red'})
+    ax.set_xlabel('X', fontdict={'size': 15, 'color': 'red'})
+
+
+
+    plt.show()
+
+
+
+draw(view_point,ori_points,new_points)