#----------------------------------------------------------------------
# Program to support simple orthographic 3D projection
#
# Copyright (C) October 2018 -- Dr. William T. Verts
#----------------------------------------------------------------------

Sine  = 0.5              # 30 degrees
Cosine= sqrt(3) / 2.0    # 30 degrees
Scale2D = 10.0
Origin2D = [0,0]

def Project3D (P3D):          #  P3D is 3D point, list [X,Y,Z]
    global Scale2D,Origin2D
    X = Origin2D[0] + (P3D[0] + P3D[2] * Cosine) * Scale2D
    Y = Origin2D[1] - (P3D[1] + P3D[2] * Sine) * Scale2D
    Result = [X,Y]
    return Result             # Result is a 2D point, list [X,Y]
    
def SetOrigin2D(P2D):
    global Origin2D
    Origin2D = P2D
    return
            
def SetScale2D(NewScale):
    global Scale2D
    Scale2D = NewScale
    return
 
def INT(N):
    return int(round(N))
                   
def addLine3D(Canvas, P0, P1, NewColor=black):     # P0 and P1 are 3D points [X,Y,Z]
    P0_2D = Project3D(P0)
    P1_2D = Project3D(P1)
    addLine(Canvas, INT(P0_2D[0]), INT(P0_2D[1]), INT(P1_2D[0]), INT(P1_2D[1]), NewColor)
    return   

def addPoint(Q0,Q1):
    X = Q0[0] + Q1[0]
    Y = Q0[1] + Q1[1]
    Z = Q0[2] + Q1[2]
    return [X,Y,Z]
    
def addHouse(Canvas, HouseOrigin, NewColor):        # HouseOrigin = [X,Y,Z] 3D point

    def Line (P0,P1):
        addLine3D(Canvas, addPoint(HouseOrigin, P0), addPoint(HouseOrigin, P1), NewColor)
        return
        
    Line([0,0,0], [6,0,0])
    Line([0,0,0], [0,3,0])
    Line([6,0,0], [6,3,0])
    Line([0,3,0], [3,4,0])
    Line([3,4,0], [6,3,0])

    Line([0,0,5], [6,0,5])
    Line([0,0,5], [0,3,5])
    Line([6,0,5], [6,3,5])
    Line([0,3,5], [3,4,5])
    Line([3,4,5], [6,3,5])
    
    Line([0,0,0], [0,0,5])
    Line([0,3,0], [0,3,5])
    Line([3,4,0], [3,4,5])
    Line([6,3,0], [6,3,5])
    Line([6,0,0], [6,0,5])
    
    return    
            
def Main():
    Canvas = makeEmptyPicture(800,600)
    SetOrigin2D([400,300])
    SetScale2D(20.0)
    addLine3D(Canvas, [10,0,0], [-10,0,0], red)
    addLine3D(Canvas, [0,10,0], [0,-10,0], green)
    addLine3D(Canvas, [0,0,10], [0,0,-10], blue)
    for X in range(-100,+100, 8):
        for Z in range(-100, +100, 8):
            addHouse(Canvas, [X,0,Z], black)
    show(Canvas)
    return