Generate triangular mesh

8/13/2019 Generate triangular mesh

1/15

CSE325Computer Science

and Sculpture

Prof. George Hart


2/15

Triangulated Surfaces

Any 3D form (polyhedral or curved) can beapproximated by a triangulated surface.

Polygons of 4 or more sides can be dividedinto triangles.

On a computer these are represented by

listing the three corners for each triangle. A corner (a vertex) is described by XYZ

coordinates


3/15

Many Triangles Allow Detail


4/15

Polygons Divide into Triangles

An n-gon is represented as n-2 triangles

4 sides2 5 sides3 8 sides6


5/15

Triangles in Space

Each vertex has (X, Y, Z)coordinates

List vertices starting with

any of the three

List counter-clockwise as

seen from outside

Normal vector points

out from object Use Right-handed XYZ

axes

Triangle:(0,0,0) (0,1,0) (0,0,1)

Or:(0,1,0) (0,0,1) (0,0,0)

Or:(0,0,1) (0,0,0) (0,1,0)


6/15

Right-Handed Coordinate System


7/15

Example Tetrahedron

A: (1 1 1) (-1 -1 1) (1 -1 -1) B: (-1 -1 1) (-1 1 -1) (1 -1 -1)

C: (1 1 1) (1 -1 -1) (-1 1 -1) D: (1 1 1) (-1 1 -1) (-1 -1 1)


8/15

Many 3D File Formats Exist 3ds 3D Studio Binary

cob Caligari objects scn Caligari

lwo, lw LightWave

obj Alias WaveFront objects

objf Stripe objf file format

off Object file format

geo AOFF File Format

raw RAW File Format

rax RAX File Format

x Direct X

wrl VRML

c4d Cinema 4D

3dm, 3dmf 3DMax

iob Imaginedxf, dxb AutoCAD DXF

3dm Rhinoceros

pro Power Render

mts Metastream fileflt OpenFlight

ase 3D Studio MAX

dwg AutoCAD DWG

ndoNendo

si SOFTIMAGE

spx SPX file format

peo, geo Homeworld

stl Stereolithography


9/15

Note: We will Simplify A Lot

Different 3D formats contain many differentways of describing not just triangles but alsopolygons, curves, colors, textures, images,

lights, cameras, animation, hierarchicalstructure, annotations, compression, and morethat is very useful in rendering images.

Well ignore all that and just look at triangles

Triangles are sufficient for describing form


10/15

stlFile Format

You can create an ASCIIstlfile in any texteditor, e.g., wordor wordpad

Then view it in any 3D viewing program.

Usually a 3D design program (e.g.,Maya)is used to create/modify/view the file, butwe will make files with a text editor as anexercise to understand the process.

Thestlfile can then be given to a solidfreeform fabrication machine to have yourform physically created.


11/15

stlFile Format

Create file in any text editor

Write a start line, an end line, and agroup of 7 lines for each triangle.

Triangles can be listed in any order.

solid

endsolid


12/15

stlFile Format

For each triangle give 7 lines:facet normal 0 0 0

outer loop

vertex X Y Z

vertex X Y Z

vertex X Y Zendloop

endfacet

Only the X Y Z parts need to change for

each triangle (Some programs need the normal)

Easy to copy and paste in editor


13/15

ExamplestlFile Format (ASCII)solid tetrahedron

facet normal 0 0 0outer loop

vertex 1 1 1

vertex 1 -1 -1

vertex -1 1 -1

endloop

endfacet

facet normal 0 0 0

outer loop

vertex 1 1 1vertex -1 1 -1

vertex -1 -1 1

endloop

endfacet

facet normal 0 0 0

outer loopvertex 1 1 1

vertex -1 -1 1

vertex 1 -1 -1

endloop

endfacet

facet normal 0 0 0

outer loop

vertex -1 1 -1

vertex 1 -1 -1vertex -1 -1 1

endloop

endfacet

endsolid tetrahedron


14/15

Lab exercise

Design an object (a pyramid; then an icosahedron)

determine coordinates of vertices

determine triangles

Create .stlfile in editor

Save it with new name, e.g.,pyramid.stl

Paste in start line, group of 7 lines, and end line

Edit it to have enough groups of 7 lines

Edit each group to have the three XYZs for onetriangle

View it in 3D viewing program

Find any problems and edit file to fix them


15/15

Demo

Creatingstlfile

Editing file

Viewing file Possible errors:

Incorrect formatting

Unmatched edges

Backwards-facing faces

Generate triangular mesh

Documents

Transcript of Generate triangular mesh