Re: 3d artifacts
- To: mathgroup at smc.vnet.net
- Subject: [mg127223] Re: 3d artifacts
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Mon, 9 Jul 2012 05:24:10 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
- References: <201207070930.FAA20625@smc.vnet.net>
Resent since this hasn't shown up. On Sat, Jul 7, 2012 at 8:14 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote: > Use Exclusions or define the functions with Piecewise > > g[t_] = -Pi/2 + Mod[t, Pi]; > > f[t_] = If[-Pi/2 <= t <= Pi/2, > (1 - Cos[2 t])/2, (-1 + Cos[2 t])/2]; > > ParametricPlot3D[{f[t] g[t], g[t]^2, f[t]}, > {t, -Pi, Pi}, Exclusions -> {-Pi/2, Pi/2}] > > f[t_] = Piecewise[ > {{(1 - Cos[2 t])/2, -Pi/2 <= t <= Pi/2}}, > (-1 + Cos[2 t])/2]; > > ParametricPlot3D[{f[t] g[t], g[t]^2, f[t]}, > {t, -Pi, Pi}] > > ww[t_] := If[0 <= t < 2 Pi, > {Cos[t], Sin[t], Sin[2 t]}, > If[2 Pi <= t <= 4 Pi, > {Sin[2 t], 15/10 Cos[t]/(1 + Sin[t]^2), Sin[t]/(1 + Sin[t]^2)}, > {Cos[t], Sin[t], Sin[2 t]}]]; > > ParametricPlot3D[ww[t], {t, 0, 4 Pi}, > Exclusions -> {2 Pi, 4 Pi}] > > ww[t_] := Piecewise[ > {{{Cos[t], Sin[t], Sin[2 t]}, > 0 <= t < 2 Pi}, > {{Sin[2 t], 15/10 Cos[t]/(1 + Sin[t]^2), Sin[t]/(1 + Sin[t]^2)}, > 2 Pi <= t <= 4 Pi}}, > {Cos[t], Sin[t], Sin[2 t]}]; > > ParametricPlot3D[ww[t], {t, 0, 4 Pi}] > > > Bob Hanlon > > > On Sat, Jul 7, 2012 at 5:30 AM, Roger Bagula <roger.bagula at gmail.com> wrote: >> In the two part defintion: >> >> f[t_] = If [ t >= -Pi/2 && t <= Pi/2, (1 - Cos[2*t])/2, (-1 + Cos[2*t])/2]; >> g[t_] = -Pi/2 + Mod[t, Pi]; >> ParametricPlot3D[{f[t]*g[t], g[t]*g[t], f[t]}, {t, -Pi, Pi}] >> >> A "handle" appears between the two parts of the curve. >> I got the same effect when I tried to get a >> patched manifold for the Whitehead Link: >> >> x = Cos[t]; >> z = Sin[t]; >> y = 2*Cos[t]*Sin[t]; >> w = {x, y, z}; >> {z1, y1} = 1/(1 + Sin[t]^2) {15/10 Cos[t], Sin[t] }; >> x1 = 2*Cos[t]*Sin[t]; >> w1 = {x1, y1, z1}; >> (* patched manifold function for Whitehead link*) >> ww[t_] := >> If[t >= 0 && t < 2*Pi, {Cos[t], Sin[t], Sin[2*t]}, >> If[t >= 2*Pi && t <= 4*Pi, {Sin[2*t], 15/10 Cos[t]/(1 + Sin[t]^2), >> Sin[t]/(1 + Sin[t]^2)}, {Cos[t], Sin[t], Sin[2*t]}]]; >> ParametricPlot3D[ww[t], {t, 0, 4*Pi + 0.01}] >> >> I'd like to remove that artifact handle >> by some simple method. >> -- Bob Hanlon
- References:
- 3d artifacts
- From: Roger Bagula <roger.bagula@gmail.com>
- 3d artifacts