Differences between revisions 9 and 10
 ⇤ ← Revision 9 as of 2009-05-21 08:01:52 → Size: 2931 Editor: pang Comment: Included "Evolutes" ← Revision 10 as of 2009-05-21 08:07:31 → ⇥ Size: 3053 Editor: pang Comment: Deletions are marked like this. Additions are marked like this. Line 35: Line 35: by Pablo Angulo. Computes the evolute of a plane curve given in parametric coordinates. The curve must be parametrized from the interval [0,2pi]. by Pablo Angulo. Computes the evolute of a plane curve given in parametric coordinates. The curve must be parametrized from the interval [0,2pi]. The following animation was done with similar code:http://www.uam.es/personal_pdi/ciencias/pangulo/adjuntos/evoluta.gif

# Sage Interactions - Geometry

## Intersecting tetrahedral reflections

by Marshall Hampton. Inspired by a question from Hans Schepker of Glass Geometry.

```#Pairs of tetrahedra, one the reflection of the other in the internal face, are joined by union operations:
p1 = Polyhedron(vertices = [[1,1,1],[1,1,0],[0,1,1],[1,0,1]])
p2 = Polyhedron(vertices = [[1/3,1/3,1/3],[1,1,0],[0,1,1],[1,0,1]])
p12 = p1.union(p2)
p3 = Polyhedron(vertices = [[0,0,1],[0,0,0],[0,1,1],[1,0,1]])
p4 = Polyhedron(vertices = [[2/3,2/3,1/3],[0,0,0],[0,1,1],[1,0,1]])
p34 = p3.union(p4)
p5 = Polyhedron(vertices = [[1,0,0],[1,0,1],[0,0,0],[1,1,0]])
p6 = Polyhedron(vertices = [[1/3,2/3,2/3],[1,0,1],[0,0,0],[1,1,0]])
p56 = p5.union(p6)
p7 = Polyhedron(vertices = [[0,1,0],[0,0,0],[1,1,0],[0,1,1]])
p8 = Polyhedron(vertices = [[2/3,1/3,2/3],[0,0,0],[1,1,0],[0,1,1]])
p78 = p7.union(p8)
pti = p12.intersection(p34).intersection(p56).intersection(p78)
@interact
def tetra_plot(opac = slider(srange(0,1.0,.25), default = .25)):
p12r = p12.render_wireframe()+p12.render_solid(opacity = opac)
p34r = p34.render_wireframe()+p34.render_solid(rgbcolor = (0,0,1),opacity = opac)
p56r = p56.render_wireframe()+p56.render_solid(rgbcolor = (0,1,0),opacity = opac)
p78r = p78.render_wireframe()+p78.render_solid(rgbcolor = (0,1,1),opacity = opac)
ptir = pti.render_wireframe()+pti.render_solid(rgbcolor = (1,0,1),opacity = .9)
show(p12r+p34r+p56r+p78r+ptir, frame = False)``` ## Evolutes

by Pablo Angulo. Computes the evolute of a plane curve given in parametric coordinates. The curve must be parametrized from the interval [0,2pi]. The following animation was done with similar code: http://www.uam.es/personal_pdi/ciencias/pangulo/adjuntos/evoluta.gif

```var('t');
def norma(v):
return sqrt(sum(x^2 for x in v))
paso_angulo=5

@interact
def _( gamma1=input_box(default=sin(t)), gamma2=input_box(default=1.3*cos(t)),
rango_angulos=range_slider(0,360,paso_angulo,(0,45),label='Draw lines for these angles') ):
print rango_angulos
gamma=(gamma1,gamma2)
gammap=(gamma.derivative(),gamma.derivative())
normal=(gammap/norma(gammap), -gammap/norma(gammap))
gammapp=(gammap.derivative(),gammap.derivative())

np=norma(gammap)
npp=norma(gammapp)
pe=gammap*gammapp+gammap*gammapp 