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345 | """
An interactive spline demo.
"""
from pscript import window
from flexx import flx
SPLINES = ['linear', 'basis', 'cardinal', 'catmullrom', 'lagrange', 'lanczos']
GENERAL_TEXT = """
The splines in this exampe are used to interpolate a line between
control points. The the range of influence is shown when a control point
is clicked. Move the control points by dragging them. Points can be
added and deleted by holding shift and clicking.
"""
LINEAR_TEXT = """
This is not really a spline, but its included for reference. Linear
interpolation is C0 continuous, and relatively easy to implement.
"""
BASIS_TEXT = """
A B-spline is a C2 continuous non-interpolating spline, used extensively
in (3D) modeling.
"""
CARDINAL_TEXT = """
A Cardinal spline is a specific type of cubic Hermite spline, and is
C1 continous. Its tension parameter makes it very versatile.
"""
CATMULLROM_TEXT = """
The Catmull–Rom spline is a Cardinal spline with a tension of 0. It is
commonly used in computer graphics to interpolate motion between key frames.
"""
LAGRANGE_TEXT = """
The Lagrange polynomials result in (C0 continous) interpolation
equivalent to Newton a polynomial. It is, however, know to suffer from
Runge's phenomenon (oscilating).
"""
LANCZOS_TEXT = """
Lanczos interpolation (C1 continous) is based on a windowed sinc
function and is usually considered to produced the best result from the
perspective of the fourier domain. It's mainly used in applications
related audio.
"""
class SplineWidget(flx.CanvasWidget):
spline_type = flx.EnumProp(SPLINES, 'cardinal', settable=True, doc="""
"The type of spline
""")
closed = flx.BoolProp(False, settable=True, doc="""
Whether the spline is closed
""")
tension = flx.FloatProp(0.5, settable=True, doc="""
The tension parameter for the Cardinal spline.
""")
_current_node = flx.Property(None, settable=True)
def init(self):
self.ctx = self.node.getContext('2d')
self.xx = [0.90, 0.80, 0.70, 0.60, 0.50, 0.40, 0.10, 0.23, 0.61, 0.88]
self.yy = [0.90, 0.60, 0.90, 0.60, 0.90, 0.70, 0.55, 0.19, 0.11, 0.38]
def factors_linear(self, t):
return [0, t, (1-t), 0]
def factors_basis(self, t):
f0 = (1 - t)**3 / 6.0
f1 = (3 * t**3 - 6 * t**2 + 4) / 6.0
f2 = (-3 * t**3 + 3 * t**2 + 3 * t + 1) / 6.0
f3 = t**3 / 6.0
return f0, f1, f2, f3
def factors_cardinal(self, t):
tension = self.tension
tau = 0.5 * (1 - tension)
f0 = - tau * (t**3 - 2 * t**2 + t)
f3 = + tau * (t**3 - 1 * t**2)
f1 = 2 * t**3 - 3 * t**2 + 1 - f3
f2 = - 2 * t**3 + 3 * t**2 - f0
return f0, f1, f2, f3
def factors_catmullrom(self, t):
f0 = - 0.5 * t**3 + 1.0 * t**2 - 0.5 * t
f1 = + 1.5 * t**3 - 2.5 * t**2 + 1
f2 = - 1.5 * t**3 + 2.0 * t**2 + 0.5 * t
f3 = + 0.5 * t**3 - 0.5 * t**2
return f0, f1, f2, f3
def factors_lagrange(self, t):
k = -1.0
f0 = t / k * (t-1) / (k-1) * (t-2) / (k-2)
k = 0
f1 = (t+1) / (k+1) * (t-1) / (k-1) * (t-2) / (k-2)
k= 1
f2 = (t+1) / (k+1) * t / k * (t-2) / (k-2)
k = 2
f3 = (t + 1) / (k+1) * t / k * (t-1) / (k-1)
return f0, f1, f2, f3
def factors_lanczos(self, t):
sin = window.Math.sin
pi = window.Math.PI
tt = (1+t)
f0 = 2*sin(pi*tt)*sin(pi*tt/2) / (pi*pi*tt*tt)
tt = (2-t)
f3 = 2*sin(pi*tt)*sin(pi*tt/2) / (pi*pi*tt*tt)
if t != 0:
tt = t
f1 = 2*sin(pi*tt)*sin(pi*tt/2) / (pi*pi*tt*tt)
else:
f1 =1
if t != 1:
tt = (1-t)
f2 = 2*sin(pi*tt)*sin(pi*tt/2) / (pi*pi*tt*tt)
else:
f2 = 1
return f0, f1, f2, f3
@flx.reaction('pointer_down')
def _on_pointer_down(self, *events):
for ev in events:
w, h = self.size
# Get closest point
closest, dist = -1, 999999
for i in range(len(self.xx)):
x, y = self.xx[i] * w, self.yy[i] * h
d = ((x - ev.pos[0]) ** 2 + (y - ev.pos[1]) ** 2) ** 0.5
if d < dist:
closest, dist = i, d
# Did we touch it or not
if dist < 9:
i = closest
if 'Shift' in ev.modifiers: # Remove point
self.xx.pop(i)
self.yy.pop(i)
self._set_current_node(None)
self.update()
else:
self._set_current_node(i)
else:
if 'Shift' in ev.modifiers:
# Add point
if not self.xx:
i = 0 # There were no points
else:
# Add in between two points. Compose the vectors
# from closest points to neightbour points and to the
# cicked point. Check with which vector the latter vector
# aligns the best by calculating their angles.
#
# Get the three points
p0 = self.xx[closest+0] * w, self.yy[closest+0] * h
if closest == 0:
p2 = self.xx[closest+1] * w, self.yy[closest+1] * h
p1 = p0[0] - (p2[0] - p0[0]), p0[1] - (p2[1] - p0[1])
elif closest == len(self.xx) - 1:
p1 = self.xx[closest-1] * w, self.yy[closest-1] * h
p2 = p0[0] - (p1[0] - p0[0]), p0[1] - (p1[1] - p0[1])
else:
p1 = self.xx[closest-1] * w, self.yy[closest-1] * h
p2 = self.xx[closest+1] * w, self.yy[closest+1] * h
# Calculate vectors, and normalize
v1 = p1[0] - p0[0], p1[1] - p0[1]
v2 = p2[0] - p0[0], p2[1] - p0[1]
v3 = ev.pos[0] - p0[0], ev.pos[1] - p0[1]
m1 = (v1[0]**2 + v1[1]**2)**0.5
m2 = (v2[0]**2 + v2[1]**2)**0.5
m3 = (v3[0]**2 + v3[1]**2)**0.5
v1 = v1[0] / m1, v1[1] / m1
v2 = v2[0] / m2, v2[1] / m2
v3 = v3[0] / m3, v3[1] / m3
# Calculate angle
a1 = window.Math.acos(v1[0] * v3[0] + v1[1] * v3[1])
a2 = window.Math.acos(v2[0] * v3[0] + v2[1] * v3[1])
i = closest if a1 < a2 else closest + 1
self.xx.insert(i, ev.pos[0] / w)
self.yy.insert(i, ev.pos[1] / h)
self._set_current_node(i)
@flx.reaction('pointer_up')
def _on_pointer_up(self, *events):
self._set_current_node(None)
@flx.reaction('pointer_move')
def _on_pointer_move(self, *events):
ev = events[-1]
if self._current_node is not None:
i = self._current_node
w, h = self.size
self.xx[i] = ev.pos[0] / w
self.yy[i] = ev.pos[1] / h
self.update()
@flx.reaction('size', 'spline_type', 'tension', 'closed', '_current_node')
def update(self, *events):
# Init
ctx = self.ctx
w, h = self.size
ctx.clearRect(0, 0, w, h)
# Get coordinates
xx = [x * w for x in self.xx]
yy = [y * h for y in self.yy]
#
if self.closed:
xx = xx[-1:] + xx + xx[:2]
yy = yy[-1:] + yy + yy[:2]
else:
xx = [xx[0] - (xx[1] - xx[0])] + xx + [xx[-1] - (xx[-2] - xx[-1])]
yy = [yy[0] - (yy[1] - yy[0])] + yy + [yy[-1] - (yy[-2] - yy[-1])]
# Draw grid
ctx.strokeStyle = '#eee'
ctx.lineWidth = 1
for y in range(0, h, 20):
ctx.beginPath()
ctx.moveTo(0, y)
ctx.lineTo(w, y)
ctx.stroke()
for x in range(0, w, 20):
ctx.beginPath()
ctx.moveTo(x, 0)
ctx.lineTo(x, h)
ctx.stroke()
# Draw nodes
ctx.fillStyle = '#acf'
ctx.strokeStyle = '#000'
ctx.lineWidth = 2
for i in range(1, len(xx)-1):
ctx.beginPath()
ctx.arc(xx[i], yy[i], 9, 0, 6.2831)
ctx.fill()
ctx.stroke()
# Select interpolation function
fun = self['factors_' + self.spline_type.lower()]
if not fun:
fun = lambda : (0, 1, 0, 0)
# Draw lines
for i in range(1, len(xx)-2):
ctx.lineCap = "round"
ctx.lineWidth = 3
ctx.strokeStyle = '#008'
support = 1 if self.spline_type == 'LINEAR' else 2
if self._current_node is not None:
if i - (support + 1) < self._current_node < i + support:
ctx.strokeStyle = '#08F'
ctx.lineWidth = 5
# Get coordinates of the four points
x0, y0 = xx[i-1], yy[i-1]
x1, y1 = xx[i+0], yy[i+0]
x2, y2 = xx[i+1], yy[i+1]
x3, y3 = xx[i+2], yy[i+2]
# Interpolate
ctx.beginPath()
# lineto = ctx.moveTo.bind(ctx)
lineto = ctx.lineTo.bind(ctx)
n = 30
for t in [i/n for i in range(n+1)]:
f0, f1, f2, f3 = fun(t)
x = x0 * f0 + x1 * f1 + x2 * f2 + x3 * f3
y = y0 * f0 + y1 * f1 + y2 * f2 + y3 * f3
lineto(x, y)
lineto = ctx.lineTo.bind(ctx)
ctx.stroke()
class Splines(flx.Widget):
def init(self):
with flx.HBox():
with flx.VBox(flex=0, minsize=150):
self.b1 = flx.RadioButton(text='Linear')
self.b2 = flx.RadioButton(text='Basis')
self.b3 = flx.RadioButton(text='Cardinal', checked=True)
self.b4 = flx.RadioButton(text='Catmull Rom')
self.b5 = flx.RadioButton(text='Lagrange')
self.b6 = flx.RadioButton(text='Lanczos')
flx.Widget(minsize=10)
closed = flx.CheckBox(text='Closed')
flx.Widget(minsize=10)
self.tension = flx.Slider(min=-0.5, max=1, value=0.5,
text=lambda: 'Tension: {value}')
flx.Widget(flex=1)
with flx.VBox(flex=1):
flx.Label(text=GENERAL_TEXT, wrap=True, style='font-size: 12px;')
self.explanation = flx.Label(text=CARDINAL_TEXT, wrap=True,
style='font-size: 12px;')
self.spline = SplineWidget(flex=1,
closed=lambda: closed.checked,
tension=lambda: self.tension.value)
LINEAR_TEXT = LINEAR_TEXT
BASIS_TEXT = BASIS_TEXT
CARDINAL_TEXT = CARDINAL_TEXT
CATMULLROM_TEXT = CATMULLROM_TEXT
LAGRANGE_TEXT = LAGRANGE_TEXT
LANCZOS_TEXT = LANCZOS_TEXT
@flx.reaction('b1.checked', 'b2.checked', 'b3.checked', 'b4.checked',
'b5.checked', 'b6.checked')
def _set_spline_type(self, *events):
ev = events[-1]
if not ev.new_value:
return # init event
type = ev.source.text.replace(' ', '')
self.spline.set_spline_type(type)
self.explanation.set_text(self[type.upper() + '_TEXT'])
@flx.reaction
def __show_hide_tension_slider(self):
if self.spline.spline_type == 'CARDINAL':
self.tension.apply_style('visibility: visible')
else:
self.tension.apply_style('visibility: hidden')
if __name__ == '__main__':
a = flx.App(Splines)
a.launch('firefox-browser')
flx.run()
|