#----------------------------------------------------------------------
# Introduction to Orthographic 3D Projections
#
# Copyright (C) April 7, 2017 -- Dr. William T. Verts
#----------------------------------------------------------------------

Origin2D = [0,0]                    # Location of [0,0,0] on canvas
Scale2D = 1.0                       # Pixels per 3D Unit
Cosine30 = cos(math.radians(30.0))  # Projection Angle
Sine30 = sin(math.radians(30.0))    # Projection Angle

def SetOrigin2D (P2D):     # Location on the canvas of the [0,0,0] point
    global Origin2D
    Origin2D = P2D
    return

def SetScale2D (N):        # Scale (size) multiplier
    global Scale2D
    Scale2D = N
    return

def Project3D (P3D):       # P3D is [X,Y,Z] in space, function returns [X,Y] on the canvas
    global Scale2D,Origin2D
    X = Origin2D[0] + (P3D[0] + P3D[2] * Cosine30) * Scale2D
    Y = Origin2D[1] - (P3D[1] + P3D[2] * Sine30)   * Scale2D
    return [X,Y]

#----------------------------------------------------------------------
# Higher level 3D geometric functions
#----------------------------------------------------------------------

def INT(N):
    return int(round(N))    
            
def addLine2D (Canvas, P1, P2, NewColor=black):     # P1 and P2 are both [X,Y] lists
    addLine(Canvas, INT(P1[0]), INT(P1[1]), INT(P2[0]), INT(P2[1]), NewColor)
    return    
    
def addLine3D (Canvas, P1, P2, NewColor=black):     # P1 and P2 are both [X,Y,Z] lists
    addLine2D (Canvas, Project3D(P1), Project3D(P2), NewColor)
    return

def addCube (Canvas, N):
    addLine3D(Canvas, [0,0,0], [N,0,0])
    addLine3D(Canvas, [0,N,0], [N,N,0])
    addLine3D(Canvas, [0,0,0], [0,N,0])
    addLine3D(Canvas, [N,0,0], [N,N,0])
        
    addLine3D(Canvas, [0,0,N], [N,0,N])
    addLine3D(Canvas, [0,N,N], [N,N,N])
    addLine3D(Canvas, [0,0,N], [0,N,N])
    addLine3D(Canvas, [N,0,N], [N,N,N])
    
    addLine3D(Canvas, [0,0,0], [0,0,N])
    addLine3D(Canvas, [N,0,0], [N,0,N])
    addLine3D(Canvas, [0,N,0], [0,N,N])
    addLine3D(Canvas, [N,N,0], [N,N,N])
    return

#----------------------------------------------------------------------
# Simple test program
#----------------------------------------------------------------------

def Main():
    Canvas = makeEmptyPicture(800,600)
    SetOrigin2D ([100,500])
    SetScale2D (4)
    show(Canvas)
    addLine3D(Canvas, [0,0,0], [100,0,0], red)
    addLine3D(Canvas, [0,0,0], [0,100,0], green)
    addLine3D(Canvas, [0,0,0], [0,0,100], blue)
    addCube(Canvas, 30)    
    repaint(Canvas)
    return