Changeset 2454 in lmdz_wrf for trunk/tools/geometry_tools.py

Timestamp:

Apr 21, 2019, 11:08:54 PM (6 years ago)

Author:

lfita

Message:

Adding:

• `p_reg_polygon': Function to provide a regular polygon of Nv vertices
• `p_reg_star': Function to provide a regular star of Nv vertices

File:

• trunk/tools/geometry_tools.py (modified) (2 diffs)

trunk/tools/geometry_tools.py

@@ -41 +41 @@
 # ellipse_polar: Function to determine an ellipse from its center and polar coordinates
 # p_circle: Function to get a polygon of a circle
+# p_reg_polygon: Function to provide a regular polygon of Nv vertices
+# p_reg_star: Function to provide a regular star of Nv vertices
 # p_square: Function to get a polygon square
 # p_spiral: Function to provide a polygon of an Archimedean spiral
@@ -511 +513 @@
 
     return spiral
+
+def p_reg_polygon(Nv, lf, N=50):
+    """ Function to provide a regular polygon of Nv vertices
+      Nv: number of vertices
+      lf: length of the face
+      N: number of points
+    """
+    fname = 'p_reg_polygon'
+
+    reg_polygon = np.zeros((N,2), dtype=np.float)
+
+    # Number of points per vertex
+    Np = N/Nv
+    # Angle incremental between vertices
+    da = 2.*np.pi/Nv
+    # Radii of the circle according to lf
+    radii = lf*Nv/(2*np.pi)
+
+    iip = 0
+    for iv in range(Nv-1):
+        # Characteristics between vertices iv and iv+1
+        av1 = da*iv
+        v1 = [radii*np.sin(av1), radii*np.cos(av1)]
+        av2 = da*(iv+1)
+        v2 = [radii*np.sin(av2), radii*np.cos(av2)]
+        dx = (v2[1]-v1[1])/Np
+        dy = (v2[0]-v1[0])/Np
+        for ip in range(Np):
+            reg_polygon[ip+iv*Np,:] = [v1[0]+dy*ip,v1[1]+dx*ip]
+
+    # Characteristics between vertices Nv and 1
+
+    # Number of points per vertex
+    Np2 = N - Np*(Nv-1)
+
+    av1 = da*Nv
+    v1 = [radii*np.sin(av1), radii*np.cos(av1)]
+    av2 = 0.
+    v2 = [radii*np.sin(av2), radii*np.cos(av2)]
+    dx = (v2[1]-v1[1])/Np2
+    dy = (v2[0]-v1[0])/Np2
+    for ip in range(Np2):
+        reg_polygon[ip+(Nv-1)*Np,:] = [v1[0]+dy*ip,v1[1]+dx*ip]
+
+    return reg_polygon
+
+def p_reg_star(Nv, lf, freq, vs=0, N=50):
+    """ Function to provide a regular star of Nv vertices
+      Nv: number of vertices
+      lf: length of the face of the regular polygon
+      freq: frequency of union of vertices ('0', for just centered to zero arms)
+      vs: vertex from which start (0 being first [0,lf])
+      N: number of points
+    """
+    fname = 'p_reg_star'
+
+    reg_star = np.zeros((N,2), dtype=np.float)
+
+    # Number of arms of the star
+    if freq != 0 and np.mod(Nv,freq) == 0: 
+        Na = Nv/freq + 1
+    else:
+        Na = Nv
+
+    # Number of points per arm
+    Np = N/Na
+    # Angle incremental between vertices
+    da = 2.*np.pi/Nv
+    # Radii of the circle according to lf
+    radii = lf*Nv/(2*np.pi)
+
+    iip = 0
+    av1 = vs*da
+    for iv in range(Na-1):
+        # Characteristics between vertices iv and iv+1
+        v1 = [radii*np.sin(av1), radii*np.cos(av1)]
+        if freq != 0:
+            av2 = av1 + da*freq
+            v2 = [radii*np.sin(av2), radii*np.cos(av2)]
+        else:
+            v2 = [0., 0.]
+            av2 = av1 + da
+        dx = (v2[1]-v1[1])/(Np-1)
+        dy = (v2[0]-v1[0])/(Np-1)
+        for ip in range(Np):
+            reg_star[ip+iv*Np,:] = [v1[0]+dy*ip,v1[1]+dx*ip]
+        if av2 > 2.*np.pi: av1 = av2 - 2.*np.pi
+        else: av1 = av2 + 0.
+
+    iv = Na-1
+    # Characteristics between vertices Na and 1
+    Np2 = N-Np*iv
+    v1 = [radii*np.sin(av1), radii*np.cos(av1)]
+    if freq != 0:
+        av2 = vs*da
+        v2 = [radii*np.sin(av2), radii*np.cos(av2)]
+    else:
+        v2 = [0., 0.]
+    dx = (v2[1]-v1[1])/(Np2-1)
+    dy = (v2[0]-v1[0])/(Np2-1)
+    for ip in range(Np2):
+        reg_star[ip+iv*Np,:] = [v1[0]+dy*ip,v1[1]+dx*ip]
+
+    return reg_star
 
 # Combined objects