#----------------------------------------------------------------------
# Introduction to 3D projections using a simple Orthographic Projection
#
# Copyright (C) November 13, 2017 -- Dr. William T. Verts
#----------------------------------------------------------------------

#----------------------------------------------------------------------
# Generic helper functions
#----------------------------------------------------------------------

def INT (N):                      # Convert float to nearest int
    return int(round(N))
    
def Radians (Degrees):            # Convert Degrees to Radians (for sin / cos)
    return Degrees / 180.0 * pi

#----------------------------------------------------------------------
# Orthographic Projection System
#
# Origin2D and Scale2D are global so that values set by SetOrigin2D
# and SetScale2D can be used by Project3D (which is the heart of the
# code here).  The projection angle is fixed at 30 degrees (which
# "looks right"), and precomputed so we don't have to compute the
# expensive sine and cosine of the same angle for every point being
# transformed.
#----------------------------------------------------------------------

Origin2D = [0,0]                  # Position on the Canvas of 3D point [0,0,0]
Scale2D  = 1.0                    # Pixels per 3D unit

Cosine30 = math.sqrt(3)/2.0       # Same as: math.cos(Radians(30.0))
Sine30   = 0.5                    # Same as: math.sin(Radians(30.0))

def Project3D (P3D):              # P3D is [X,Y,Z], returns a 2D point [X,Y]
    global Origin2D, Scale2D
    XOffset = P3D[0] + P3D[2] * Cosine30
    YOffset = P3D[1] + P3D[2] * Sine30
    X = Origin2D[0] + XOffset * Scale2D
    Y = Origin2D[1] - YOffset * Scale2D
    return [X,Y]
     
def SetOrigin2D (P2D):            # P2D is [X,Y] indicating location on canvas of [0,0,0]
    global Origin2D
    Origin2D = P2D    
    return

def SetScale2D (N):               # N is number of pixels per 3D Unit
    global Scale2D
    Scale2D = N
    return
        
#----------------------------------------------------------------------
# Start building tools to use the 3D system.
# addLine3D draws a line between two 3D points.
#----------------------------------------------------------------------

def addLine3D(Canvas, P0, P1, NewColor=black):    #  P0 and P1 are both [X,Y,Z] points
    Q0 = Project3D(P0)                            #  Q0 and Q1 are both [X,Y] points
    Q1 = Project3D(P1)
    addLine(Canvas, INT(Q0[0]), INT(Q0[1]), INT(Q1[0]), INT(Q1[1]), NewColor)
    return
                
#----------------------------------------------------------------------
# Test program showing how to use the 3D projection system.
# Once the canvas has been set up and the position and scale of
# the 3D system have been set, the rest of the program is entirely
# expressed in 3D.
#----------------------------------------------------------------------

def Main():
    Canvas = makeEmptyPicture(400,300)
    SetOrigin2D([getWidth(Canvas)/2, getHeight(Canvas)/2])
    SetScale2D(10.0)
    addLine3D(Canvas, [-10,0,0], [+10,0,0], red)      # X axis
    addLine3D(Canvas, [0,-10,0], [0,+10,0], green)    # Y axis
    addLine3D(Canvas, [0,0,-10], [0,0,+10], blue)     # Z axis
    show(Canvas)
    return