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Creating Tactile Captions In Three-Dimensional Computer- Aided Design Stewart Dickson, Visualization Researcher Computer Science and Mathematics Division

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u1[a_,b_] := 0.5 (e (a + I*b) + e (- a - I*b) ) u2[a_,b_] := 0.5 (e (a + I*b) - e (- a - I*b) ) z1k[a_,b_,n_,k_] := e (k*2*Pi*I/n) *u1[a,b] (2.0/n) z2k[a_,b_,n_,k_] := e (k*2*Pi*I/n) *u2[a,b] (2.0/n) {x, y, z} -> { Re[z1k[a,b,n,k1]], Re[z2k[a,b,n,k2]], Cos[alpha]*Im[z1k[a,b,n,k1]] + Sin[alpha]*Im[z2k[a,b,n,k2]]} a: (-1.0,1.0); b:(0, Pi/2); k2: (0, n - 1) k1: (0, n - 1) Creating Tactile Mathematics Calabi-Yau Manifold (with Andrew Hanson)

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r1 = 1.0 r2 = 3.0 Bx [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Cos[u/3.0] By [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Sin[u/3.0] Bz [u_, v_] := r1 * Sin[u/2.0] x [u_, v_] := N[Bx [u, v]] + r1 * Cos[u/3.0] * Cos[v - Pi] y [u_, v_] := N[By [u, v]] + r1 * Sin[u/3.0] * Cos[v - Pi] z [u_, v_] := N[Bz [u, v]] + r1 * Sin[v - Pi] Trefoil Torus-Knot: TactileMathematics

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Nude in a Red Armchair" by Pablo Picasso, Original image provided by the Tate Museum.

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Molecular diagram

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Sheet music made tactile on Tiger for example

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Tactile Microscopy

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Tactile Chemical Modeling

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Molecular SLA Models

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“The Optiverse” (1998) by George Francis, John Sullivan, Stuart Levy

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“The Optiverse” (1998) by George Francis, John Sullivan, Stuart Levy

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Physical Models from Scientific Simulation

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Physical Models from Scientific Simulation

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Physical Models from Scientific Simulation

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Professor Bernard Morin

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Captions on a Mathematical Surface in Computer Graphics

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Captions on a Tactile Mathematical Surface

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DotsPlus Braille Captions on a Mathematical Surface

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Parametric Surface Implicit Surface Thicken STL File Steps to Tactile Mathematics Slice and Build Captions CAD

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Thickening a Polygon Mesh in CAD -V0’ = V0 - t X N0 V0’ = V0 + t X N V0 V1 V2 -N0 -N1 N1 -V1’ -V2’

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Documentation: DotsPlus ®

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Documentation: DotsPlus ® 3-D

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3-D Braille Dot Geometry in CAD

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3-D Braille Typesetting in CAD

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3-D Braille Typesetting in CAD

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3-D Braille Typesetting in CAD/CAM

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Braille Typesetting in 3-D CAD

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U N V Local, Parametric Coordinate Space

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ParaMeshMap for Open Inventor TM

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Problems with Current Tools Maya Creep Node requires NURBS Surfaces NURBS Surfaces do not port to Rapid Prototyping Scientific Visualization does not produce NURBS Surfaces Proposed Solution Pseudo Curve-on-Polygon Surface (X 4) -> Parametric Region -> SoQuadMesh or NURBS -> Creep/ParaMeshMap

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Version 0.1 MacOS-X 10.2 PPC DotsPlus ® 3-D for Alias Maya Open Inventor TM Apple MacOS-X Linux i386 SGI Irix 6.5

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Science Access Research sponsored by Computer Science and Mathematics Division of Oak Ridge National Laboratory, managed by UT-Battelle, LLC for the U.S. DOE under Contract No. DE-AC05-00OR22725.

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References: Stephen Wolfram, The Mathematica Book, John M. Sullivan, George Francis and Stuart Levy, "The Optiverse", Stewart Dickson, "Braille-Annotated Tactile Models …", Steven Wilkinson, 3D Plots of Implicitly Defined Surfaces, Z Corporation, 3-D Printing 3D Systems, Stereolithography

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References, Continued: Stratasys, Fused Deposition Modeling Marshall Burns, The StL Standard Data Format for Fabbers Mark Preddy, John Gardner, Steve Sahyun, and Dave Skrivanek Dotsplus, CSUN Conference, March Stewart Dickson, "DotsPlus 3-D for Maya", Stewart Dickson, "Braille Typesetting in 3-D …",

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References, Continued: Stewart Dickson, "fromThreeScript", "Thicken", "tostl”, "ParaMeshMap". Les Piegl, Wayne Tiller; The NURBS Book; New York: Springer-Verlag, 1997; ISBN: Side Effects Software, Inc.

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