Vertices have position, normal, colour, texture coordinates, etc.

Stanford bunny

Surface is

from Blender	from 3dsMax

Rendered as a small disk, with lighting

Image from "Interpolatory Refinement for Real-Time Processing of Point-Based Geometry" by Guennebaud, Barthe, and Paulin, EuroGraphics 2005

Image mesh from hal.inria.fr/inria-00417371

Image from wikipedia.org

A 3D array of scalar values

From cabiatl.com/mricro/mricro/render

List of vertices: $v_0, v_1, v_2, \ldots$

List of faces: $f_0, f_1, f_2, \ldots$

$v_i$ has position $(x,y,z)$, normal $(n_x, n_y, n_z)$, colour $(r,g,b)$, texture coordinates $(s,t)$.

$f_i$ has vertices $v_{i_0}, v_{i_1}, v_{i_2}$ and normal $n$.

Render by (slowly) iterating through all faces.

Good for topological queries (e.g. what faces are adjace to a vertex, what edges are around a face (in order)).

Edges are unidirectional.

Each edge $e_L$ stores pointers to:

$v_T$	tail vertex
$e_R$	twin edge in other direction
$f_L$	face to left of edge
$e_{ccw}$	next outgoing edge counterclockwise at tail vertex

Each face $f$ stores a pointer to any adjacent edge.

Each vertex $v$ stores a pointer to any adjacent outgoing edge.

Queries

Topological Surgery

Rendering $n$ triangles using "triangle soup" processes $3n$ vertices.

Using $k$ triangle strips for the same $n$ triangles processes $n + 2k$ vertices: $2$ to start the strip plus $1$ more for each triangle on the strip.

Covering a triangle mesh with a minimum number of strips is NP-hard.

To render, openGL needs to know whether the next triangle is to the right or the left exit from the current triangle:

Option 1: Add a bit to indicate left or right.

Option 2: Assume alternating left, then right, then left, etc.: Sequence is $v_0, v_1, v_2, \ldots, v_9$.

Option 3: Add empty triangles: Sequence is $v_0, v_1, v_2, \ldots, v_7$.