init_code

pygarment/pattern/utils.py

@@ -0,0 +1,85 @@
+"""Generic utility functions"""
+
+import numpy as np
+
+def list_to_c(num):
+    """Convert 2D list or list of 2D lists into complex number/list of complex numbers"""
+    if isinstance(num[0], list) or isinstance(num[0], np.ndarray):
+        return [complex(n[0], n[1]) for n in num]
+    else: 
+        return complex(num[0], num[1])
+    
+def c_to_np(num):
+    """Convert complex number to a numpy array of 2 elements"""
+    return np.asarray([num.real, num.imag])
+
+def vector_angle(v1, v2):
+    """Find an angle between two 2D vectors"""
+    v1, v2 = np.asarray(v1), np.asarray(v2)
+    cos = np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))
+    cos = max(min(cos, 1), -1)  # NOTE: getting rid of numbers like 1.000002 that appear due to numerical instability
+    angle = np.arccos(cos) 
+    # Cross to indicate correct relative orienataion of v2 w.r.t. v1
+    cross = np.cross(v1, v2)
+    
+    if abs(cross) > 1e-5:
+        angle *= np.sign(cross)
+    return angle
+
+def c_to_list(num):
+    """Convert complex number to a list of 2 elements
+        Allows processing of lists of complex numbers
+    """
+
+    if isinstance(num, (list, tuple, set, np.ndarray)):
+        return [c_to_list(n) for n in num]
+    else:
+        return [num.real, num.imag]
+    
+def close_enough(f1, f2=0, tol=1e-4):
+    """Compare two floats correctly """
+    return abs(f1 - f2) < tol
+
+# Vector local coodinates conversion
+def rel_to_abs_2d(start, end, rel_point):
+    """
+        Converts coordinates expressed in a coordinate frame local
+        to the edge [start, end] into edge vertices (global) coordinate frame
+    """
+
+    start, end = np.array(start), np.array(end)  # in case inputs are lists/tuples
+    edge = end - start
+    edge_perp = np.array([-edge[1], edge[0]])
+
+    abs_start = start + rel_point[0] * edge
+    abs_point = abs_start + rel_point[1] * edge_perp
+
+    return abs_point
+
+def abs_to_rel_2d(start, end, abs_point, as_vector=False):
+    """
+        Converts coordinates expressed in a global coordinate frame into 
+        a frame local to the edge [start, end] 
+    """
+
+    start, end, abs_point = np.array(start), np.array(end), \
+        np.array(abs_point)
+
+    rel_point = [None, None]
+    edge_vec = end - start
+    edge_len = np.linalg.norm(edge_vec)
+    point_vec = abs_point if as_vector else abs_point - start  # vector or point
+    
+    # X
+    # project control_vec on edge_vec by dot product properties
+    projected_len = edge_vec.dot(point_vec) / edge_len 
+    rel_point[0] = projected_len / edge_len
+    # Y
+    projected = edge_vec * rel_point[0]
+    vert_comp = point_vec - projected  
+    rel_point[1] = np.linalg.norm(vert_comp) / edge_len
+
+    # Distinguish left&right curvature
+    rel_point[1] *= np.sign(np.cross(edge_vec, point_vec))
+
+    return np.asarray(rel_point)