examples.txt

# apply a rotation affine transformation to a point
# =================================================
p = Point(6,0,label='p')
T = AffineT.rotation(45)
p2 = T * p
p2.label = 'p2'

draw(p,p2,T)

# visualize vector addition
# =========================
v = Vector(6,0,label='v')
v2 = Vector(0,3,label='v2')
v3 = v + v2
v3.label = 'sum'

draw(v,v2,v3)

# visualize dot product
# =====================
v = Vector(1,1)
v.magnitude = 5
v.angle = 0

v2 = Vector(1,1)
v2.magnitude = 5
v2.angle = 0

def on_update(dt):
  v2.angle += dt * 20 # turn 20 degrees per second
  dot = int(v.dot(v2)) # dot product between v and v2 (rounded to an int)
  v2.label = str(dot)

draw(v,v2)

# visualize mapping between coordinate systems
# ============================================

# new space to original space
newspace = AffineT.translation(6,4) * AffineT.rotation(45)
p = Point(1,1)
to_original_space = newspace * p
to_original_space.label = '(1,1) from newspace to original'
print(to_original_space)

# original space to new space
T = newspace**-1
to_new_space = T * to_original_space
to_new_space.label = 'back to newspace'
print(to_new_space)

draw(newspace,to_original_space,to_new_space)

# draw a parametrized curve (circle)
# ==================================
v = Vector(1,1)
v.magnitude = 5
t = 0
h = v.magnitude

polyline = Polyline()
def on_update(dt):
  global t

  v.angle = t

  theta = radians(t)
  x = h * math.cos(theta)  
  y = h * math.sin(theta)
  polyline.add((x,y))
  
  t += 10 * dt # increment t 10 per second

draw(v,polyline)

# draw a flower using parametrized curves
# =======================================
v = Vector(1,1)
v.magnitude = 5
t = 0
h = v.magnitude

polyline = Polyline()
polyline.color = 'purple'
def on_update(dt):
  global t
  global h

  h = math.sin(0.1*t) * 5 + 2

  theta = radians(t)
  x = h * math.cos(theta)  
  y = h * math.sin(theta)
  polyline.add((x,y))

  v.angle = t
  v.magnitude = h
  
  t += 30 * dt # increment t 30 per second

draw(v,polyline)