Plot3D.py

from vpython import *
scene.width = scene.height = 600
# There is an L by L grid of vertex objects, numbered 0 through L-1 by 0 through L-1.
# Only the vertex operators numbered L-2 by L-2 are used to create quads.
# The extra row and extra column of vertex objects simplifies edge calculations.
# The stride length from y = 0 to y = 1 is L.
L = 50
scene.center = vec(0.05*L,0.2*L,0)
scene.range = 1.3*L
## The next line contains LaTeX math notation. See http://www.glowscript.org/docs/VPythonDocs/MathJax.html
#scene.caption = """\\( f(x,y,t) = 0.7+0.2\\sin{(10x)}\\cos{(10y)}\\cos{(2t)} \\)
scene.caption = """<i>f</i>(<i>x,y,t</i>) = 0.7+0.2sin(10<i>x</i>)cos(10<i>y</i>)cos(2<i>t</i>)
<b>Click to toggle between pausing or running.</b>
In GlowScript programs:
   Right button drag or Ctrl-drag to rotate "camera" to view scene.
   To zoom, drag with mid1e button or Alt/Option depressed, or use scroll wheel.
     On a two-button mouse, midd1e is left + right.
   Touch screen: pinch/extend to zoom, swipe or two-finger rotate."""
#MathJax.Hub.Queue(["Typeset",MathJax.Hub]) # format the LaTeX; see http://www.glowscript.org/docs/VPythonDocs/MathJax.html

class plot3D:
    def __init__(self, f, xmin, xmax, ymin, ymax, zmin, zmax):
        # The x axis is labeled y, the z axis is labeled x, and the y axis is labeled z.
        # This is done to mimic fairly standard practive for plotting
        #     the z value of a function of x and y.
        self.f = f
        if not xmin: self.xmin = 0
        else: self.xmin = xmin
        if not xmax: self.xmax = 1
        else: self.xmax = xmax
        if not ymin: self.ymin = 0
        else: self.ymin = ymin
        if not ymax: self.ymax = 1
        else: self.ymax = ymax
        if not zmin: self.zmin = 0
        else: self.zmin = zmin
        if not zmax: self.zmax = 1
        else: self.zmax = zmax
        
        R = L/100
        d = L-2
        xaxis = cylinder(pos=vec(0,0,0), axis=vec(0,0,d), radius=R, color=color.yellow)
        yaxis = cylinder(pos=vec(0,0,0), axis=vec(d,0,0), radius=R, color=color.yellow)
        zaxis = cylinder(pos=vec(0,0,0), axis=vec(0,d,0), radius=R, color=color.yellow)
        k = 1.02
        h = 0.05*L
        text(pos=xaxis.pos+k*xaxis.axis, text='x', height=h, align='center', billboard=True, emissive=True)
        text(pos=yaxis.pos+k*yaxis.axis, text='y', height=h, align='center', billboard=True, emissive=True)
        text(pos=zaxis.pos+k*zaxis.axis, text='z', height=h, align='center', billboard=True, emissive=True)
    
        self.vertices = []
        for x in range(L):
            for y in range(L):
                val = self.evaluate(x,y)
                self.vertices.append(self.make_vertex( x, y, val ))
        
        self.make_quads()
        self.make_normals()
        
    def evaluate(self, x, y):
        d = L-2
        return (d/(self.zmax-self.zmin)) * (self.f(self.xmin+x*(self.xmax-self.xmin)/d, self.ymin+y*(self.ymax-self.ymin)/d)-self.zmin)
    
    def make_quads(self):
        # Create the quad objects, based on the vertex objects already created.
        for x in range(L-2):
            for y in range(L-2):
                v0 = self.get_vertex(x,y)
                v1 = self.get_vertex(x+1,y)
                v2 = self.get_vertex(x+1, y+1)
                v3 = self.get_vertex(x, y+1)
                quad(vs=[v0, v1, v2, v3])
        
    def make_normals(self):
        # Set the normal for each vertex to be perpendicular to the lower left corner of the quad.
        # The vectors a and b point to the right and up around a vertex in the xy plance.
        for i in range(L*L):
            x = int(i/L)
            y = i % L
            if x == L-1 or y == L-1: continue
            v = self.vertices[i]
            a = self.vertices[i+L].pos - v.pos
            b = self.vertices[i+1].pos - v.pos
            v.normal = cross(a,b)
    
    def replot(self):
        for i in range(L*L):
            x = int(i/L)
            y = i % L
            v = self.vertices[i]
            v.pos.y = self.evaluate(x,y)
        self.make_normals()
                
    def make_vertex(self,x,y,value):
        return vertex(pos=vec(y,value,x), color=color.cyan, normal=vec(0,1,0))
        
    def get_vertex(self,x,y):
        return self.vertices[x*L+y]
        
    def get_pos(self,x,y):
        return self.get_vertex(x,y).pos

t = 0
dt = 0.02
def f(x, y):
    # Return the value of the function of x and y:
    return 0.7+0.2*sin(10*x)*cos(10*y)*sin(5*t)

p = plot3D(f, 0, 1, 0, 1, 0, 1) # function, xmin, xmax, ymin, ymax (defaults 0, 1, 0, 1, 0, 1)

run = True
def running(ev):
    global run
    run = not run

scene.bind('mousedown', running)
scene.forward = vec(-0.7,-0.5,-1)

while True:
    rate(30)
    if run:
        p.replot()
        t += dt