# Oblique.py
# M.Lampton UCB SSL  2016

import numpy as np
import matplotlib.patches as patches
import matplotlib.pyplot as plt

# Set up the parameters of the square surface to plot

NSIDE = 100       # samples per side of square
XPEAK = 56.1      # x location of peak 
YPEAK = 66.2      # y location of peak
ZPEAK = 88.0      # height of peak
NOISE = 1.0       # rms noise in surface
RHALF = 4.0       # radius of peak at half intensity
SHELF = 5.0       # pedestal height above zero level
FLOOR = -5.0      # floor of polygons


# Define the surface and the mapping of {x,y,z} onto screen {h,v} coordinates

def zfunc(x, y):
    if y==0 or y==NSIDE-1:
        return FLOOR
    r2 = ((x-XPEAK)**2 + (y-YPEAK)**2)/RHALF**2
    r4 = r2**2
    return SHELF + NOISE*np.random.normal() + ZPEAK/(1+r4)
    
def getHoriz(x,y): 
    return x+y 
    
def getVert(x,y,z):
    return -0.5*x + 0.5*y + z

# All set. Do the plot

fig = plt.figure()
ax = fig.add_subplot(111)
for x in range(0, NSIDE):
    vertices = np.zeros(shape=(NSIDE,2))
    for y in range(0, NSIDE):
        vertices[y] = (getHoriz(x,y), getVert(x,y,zfunc(x,y)))
    poly = patches.Polygon(vertices, facecolor=(0.,0.,1.), edgecolor=(1.,1.,1))
    ax.add_patch(poly)
    
ax.set_xlim(-10, 210)
ax.set_ylim(-70, 120)
plt.show()