def draw_spring(spring,size,color,level):
p = point.with_components(spring.mass[0].get_position().components())
q = point.with_components(spring.mass[1].get_position().components())
p.z = 0.1 * level
q.z = 0.1 * level
glColor3f(color[0],color[1],color[2])
deform = max(min(spring.get_deformation(),10.0),0.333333)
draw_line(p,q,size/deform)
def make_cyl(s):
fs = []
step = 3+s
# Center points of circular faces (front and back) in the x-y plane
ccf = point.with_components( [ 0.0, 0.0, 1.0] )
ccb = point.with_components( [ 0.0, 0.0,-1.0] )
# Constructs triangle mesh by looping completely around a circle using a specified number of steps (sides).
# Each loop specifies 4 points, two on the front circle and two on the back;
# then two facets are made using the center point of a circular face and the two corresponding points.
# Another two facets are made for the cylinder's sides by dividing the rectangle of 4 specified points in half.
for i in range(0,step):
x_i = cos(2*pi*i/step)
x_j = cos(2*pi*(i+1)/step)
y_i = sin(2*pi*i/step)
y_j = sin(2*pi*(i+1)/step)
pf_i = point.with_components( [ x_i, y_i, 1] )
pf_j = point.with_components( [ x_j, y_j, 1] )
pb_i = point.with_components( [ x_i, y_i,-1] )
pb_j = point.with_components( [ x_j, y_j,-1] )
c1 = color(abs(x_i),abs(y_i),0.75)
c2 = color(abs(x_j),abs(y_j),0.25)
fs.extend( [ facet(ccf,pf_i,pf_j,c1), facet(ccb,pb_i,pb_j,c2), facet(pf_i,pf_j,pb_i,c1), facet(pb_i,pb_j,pf_j,c2) ] )
return fs
def draw_mass(mass,size,color,level):
p = point.with_components(mass.get_position().components())
p.z = 0.1 * level
glColor3f(color[0],color[1],color[2])
draw_disk(p,size/2.0*mass.get_mass())
def make_cube():
fs = []
# Time/energy permitting -- iterate
c0 = color(0.25,0.0,0.0)
p00 = point.with_components( [ 1.0,-1.0, 1.0] )
p01 = point.with_components( [-1.0,-1.0, 1.0] )
p02 = point.with_components( [-1.0, 1.0, 1.0] )
f0 = facet(p00,p01,p02,c0)
fs.append(f0)
c1 = color(0.5,0.0,0.0)
p10 = point.with_components( [ 1.0,-1.0, 1.0] )
p11 = point.with_components( [ 1.0, 1.0, 1.0] )
p12 = point.with_components( [-1.0, 1.0, 1.0] )
f1 = facet(p10,p11,p12,c1)
fs.append(f1)
c2 = color(0.75,0.0,0.0)
p20 = point.with_components( [ 1.0,-1.0,-1.0] )
p21 = point.with_components( [ 1.0, 1.0, 1.0] )
p22 = point.with_components( [ 1.0,-1.0, 1.0] )
f2 = facet(p20,p21,p22,c2)
fs.append(f2)
c3 = color(1.0,0.0,0.0)
p30 = point.with_components( [ 1.0, 1.0,-1.0] )
p31 = point.with_components( [ 1.0,-1.0,-1.0] )
p32 = point.with_components( [ 1.0, 1.0, 1.0] )
f3 = facet(p30,p31,p32,c3)
fs.append(f3)
c4 = color(0.0,0.25,0.0)
p40 = point.with_components( [ 1.0, 1.0, 1.0] )
p41 = point.with_components( [-1.0, 1.0,-1.0] )
p42 = point.with_components( [-1.0, 1.0, 1.0] )
f4 = facet(p40,p41,p42,c4)
fs.append(f4)
c5 = color(0.0,0.5,0.0)
p50 = point.with_components( [ 1.0, 1.0,-1.0] )
p51 = point.with_components( [-1.0, 1.0,-1.0] )
p52 = point.with_components( [ 1.0, 1.0, 1.0] )
f5 = facet(p50,p51,p52,c5)
fs.append(f5)
c6 = color(0.0,0.75,0.0)
p60 = point.with_components( [-1.0, 1.0,-1.0] )
p61 = point.with_components( [-1.0,-1.0,-1.0] )
p62 = point.with_components( [-1.0,-1.0, 1.0] )
f6 = facet(p60,p61,p62,c6)
fs.append(f6)
c7 = color(0.0,1.0,0.0)
p70 = point.with_components( [-1.0, 1.0,-1.0] )
p71 = point.with_components( [-1.0,-1.0, 1.0] )
p72 = point.with_components( [-1.0, 1.0, 1.0] )
f7 = facet(p70,p71,p72,c7)
fs.append(f7)
c8 = color(0.0,0.0,0.25)
p80 = point.with_components( [-1.0,-1.0,-1.0] )
p81 = point.with_components( [ 1.0,-1.0, 1.0] )
p82 = point.with_components( [-1.0,-1.0, 1.0] )
f8 = facet(p80,p81,p82,c8)
fs.append(f8)
c9 = color(0.0,0.0,0.5)
p90 = point.with_components( [ 1.0,-1.0,-1.0] )
p91 = point.with_components( [ 1.0,-1.0, 1.0] )
p92 = point.with_components( [-1.0,-1.0,-1.0] )
f9 = facet(p90,p91,p92,c9)
fs.append(f9)
c10 = color(0.0,0.0,0.75)
p100 = point.with_components( [-1.0, 1.0,-1.0] )
p101 = point.with_components( [-1.0,-1.0,-1.0] )
p102 = point.with_components( [ 1.0,-1.0,-1.0] )
f10 = facet(p100,p101,p102,c10)
fs.append(f10)
c11 = color(0.0,0.0,1.0)
p110 = point.with_components( [ 1.0,-1.0,-1.0] )
p111 = point.with_components( [-1.0, 1.0,-1.0] )
p112 = point.with_components( [ 1.0, 1.0,-1.0] )
f11 = facet(p110,p111,p112,c11)
fs.append(f11)
return fs
def make_fromOBJ(filename):
# Makes triangle mesh from OBJ file.
# Only processes vertex and facet info; ignores the rest
vs,ps = [None],[None] # Occupy index 0 so vertex indices match
fs = []
cmax = 0 # Max coordinate value found in file; used for scaling
hue = [random(),random(),random()]
try:
with open(filename, 'r') as fi:
vsDone = False
for line in fi:
# Remove whitespace in line and split by term
l = line.rstrip()
terms = l.split(" ")
# Line represents a vertex
if terms[0] == "v":
p = []
for i in range(1,len(terms)):
if abs(float(terms[i])) > cmax:
cmax = abs(float(terms[i]))
p.append(float(terms[i]))
ps.append(p)
# Line represents a facet
elif terms[0] == "f":
# Scale all vertex coordinates before making facets
# (bunny is super small and teapot is super not otherwise)
if not vsDone:
for i in range(1,len(ps)):
for n,coord in enumerate(ps[i]):
ps[i][n] = 1.5*coord/cmax
v = point.with_components(ps[i])
vs.append(v)
vsDone = True
# Get vertices
v1 = vs[int(terms[1])]
v2 = vs[int(terms[2])]
v3 = vs[int(terms[3])]
if len(terms) == 5:
# If 4 vertices specified for a facet,
# split into two.
# More can be specified but they won't be handled
v4 = vs[int(terms[4])]
c1 = getColor(v1,v2,v3,hue)
c2 = getColor(v4,v2,v3,hue)
f1 = facet(v1,v2,v3,c1)
f2 = facet(v4,v2,v3,c2)
fs.extend([f1,f2])
else:
c = getColor(v1,v2,v3,hue)
f = facet(v1,v2,v3,c)
fs.append(f)
except IOError:
print("Could not read file: ", filename)
return fs
def make_tetra():
# Make a tetrahedron.
fs = []
# missing ---
c0 = color(1.0,1.0,0.0)
p00 = point.with_components( [ 1.0,-1.0, 1.0] )
p01 = point.with_components( [ 1.0, 1.0,-1.0] )
p02 = point.with_components( [-1.0, 1.0, 1.0] )
f0 = facet(p00,p01,p02,c0)
fs.append(f0)
# missing ++-
c1 = color(0.0,1.0,1.0)
p10 = point.with_components( [ 1.0,-1.0, 1.0] )
p11 = point.with_components( [-1.0, 1.0, 1.0] )
p12 = point.with_components( [-1.0,-1.0,-1.0] )
f1 = facet(p10,p11,p12,c1)
fs.append(f1)
# missing -++
c2 = color(1.0,0.0,1.0)
p20 = point.with_components( [-1.0,-1.0,-1.0] )
p21 = point.with_components( [ 1.0, 1.0,-1.0] )
p22 = point.with_components( [ 1.0,-1.0, 1.0] )
f2 = facet(p20,p21,p22,c2)
fs.append(f2)
# missing +-+
c3 = color(1.0,1.0,1.0)
p30 = point.with_components( [ 1.0, 1.0,-1.0] )
p31 = point.with_components( [-1.0,-1.0,-1.0] )
p32 = point.with_components( [-1.0, 1.0, 1.0] )
f3 = facet(p30,p31,p32,c3)
fs.append(f3)
return fs
def make_torus(s):
fs = []
step = 3+s
minr = 0.5 # Minor radius // Requires minr < majR to work as intended.
majR = 1 # Major radius //
rings = []
ucirc = []
# Calculate all the vertices for the mesh by making rings of points
# (circles with r=0.5, starting in the x-y plane),
# rotating CCW about the y-axis.
for i in range(0,step):
ps = []
if i == 0:
# Unit circle in x-y plane centered at (1,0,0)
for n in range(0,step):
x = (majR-minr)*cos(2*pi*n/step)+majR
y = (majR-minr)*sin(2*pi*n/step)
z = 0
p = [x,y,z]
ucirc.append(p)
rings.append(ucirc)
else:
angle = 2*pi*i/step
# Rotation matrix
r = [[cos(angle),0,sin(angle)],[0,1,0],[-sin(angle),0,cos(angle)]]
for n in range(0,step):
# Rotate the nth point on the unit circle
p = dot(ucirc[n],r)
ps.append(p)
rings.append(ps)
rings.append(rings[0])
# For every ring,
for r in range(0,len(rings)-1):
# for every point in that ring,
for p in range(0,len(rings[r])):
# take the next point on that ring
# and two corresponding points on an adjacent (CCW) ring
# (wrap around if it's the last point),
if p == len(rings[r])-1:
r0p0 = point.with_components(rings[r][p])
r0p1 = point.with_components(rings[r][0])
r1p0 = point.with_components(rings[r+1][p])
r1p1 = point.with_components(rings[r+1][0])
else:
r0p0 = point.with_components(rings[r][p])
r0p1 = point.with_components(rings[r][p+1])
r1p0 = point.with_components(rings[r+1][p])
r1p1 = point.with_components(rings[r+1][p+1])
# make two colours based on the positions of two of those points
# (one per ring),
c0 = color(abs(r0p0[0]-1),abs(r0p0[1]),abs(r0p0[2])/2)
c1 = color(abs(r1p1[0]-1),abs(r1p1[1]),abs(r1p1[2])/2)
# and make two facets from those points and colors.
f0 = facet(r0p0,r0p1,r1p0,c0)
f1 = facet(r1p0,r1p1,r0p1,c1)
fs.extend([f0,f1])
return fs
def make_sphere(s):
fs,cs = [],[]
step = 3+s
# Generate colors
for i in range(0,2*step):
cr = abs(cos(i*pi/(2*step)))
cg = abs(sin(i*pi/(2*step)))
cb = abs(tan(i*pi/(2*step)))
cs.append(color(cr,cg,cb))
# Points at N-S poles
pN = point.with_components( [ 0.0, 1.0, 0.0] )
pS = point.with_components( [ 0.0,-1.0, 0.0] )
# Generate mesh by making triangle fans at the poles
# and latitudinal triangle strips elsewhere.
for i in range(0,step+1):
j = i+1 # 'i' signifies current ring, 'j' next ring
# y-position for i- and j-rings
y_i = cos(i*pi/step)
y_j = cos(j*pi/step)
# Radii for i- and j-rings
r_i = abs(sin(i*pi/step))
r_j = abs(sin(j*pi/step))
# Make triangles
for m in range(0,step):
n = m+1
if i == 0 or i == step:
# If at the poles, make a fan
r = sin(pi/step)
x_m = r*cos(2*pi*m/step)
x_n = r*cos(2*pi*n/step)
z_m = r*sin(2*pi*m/step)
z_n = r*sin(2*pi*n/step)
p_m = point.with_components( [ x_m, y_j, z_m ] )
p_n = point.with_components( [ x_n, y_j, z_n ] )
if i == 0:
f = facet(pN,p_m,p_n,cs[0])
else:
f = facet(pS,p_m,p_n,cs[2*step-1])
fs.append(f)
else:
# Otherwise, make a latitudinal strip
x_m = cos(2*pi*m/step)
x_n = cos(2*pi*n/step)
z_m = sin(2*pi*m/step)
z_n = sin(2*pi*n/step)
p_im = point.with_components( [ r_i*x_m, y_i, r_i*z_m ] )
p_in = point.with_components( [ r_i*x_n, y_i, r_i*z_n ] )
p_jm = point.with_components( [ r_j*x_m, y_j, r_j*z_m ] )
p_jn = point.with_components( [ r_j*x_n, y_j, r_j*z_n ] )
f1 = facet(p_im,p_in,p_jm,cs[2*i])
f2 = facet(p_jm,p_jn,p_in,cs[2*i+1])
fs.extend([f1,f2])
return fs