In computer graphics, a triangle strip is a subset of triangles in a triangle mesh with shared vertices, and is a more memory-efficient method of storing information about the mesh. They are more efficient than un-indexed lists of triangles, but usually equally fast or slower than indexed triangle lists. The primary reason to use triangle strips is to reduce the amount of data needed to create a series of triangles. The number of vertices stored in memory is reduced from to , where is the number of triangles to be drawn. This allows for less use of disk space, as well as making them faster to load into RAM.
For example, the four triangles in the diagram, without using triangle strips, would have to be stored and interpreted as four separate triangles: ABC, CBD, CDE, and EDF. However, using a triangle strip, they can be stored simply as a sequence of vertices ABCDEF. This sequence would be decoded as a set of triangles with vertices at ABC, BCD, CDE and DEF - although the exact order that the vertices are read will not be in left-to-right order as this would result in adjacent triangles facing alternating directions.
OpenGL implementation
OpenGL has built-in support for triangle strips. Fixed function OpenGL (deprecated in OpenGL 3.0) has support for triangle strips using immediate mode and the , , and functions. Newer versions support triangle strips using and .
To draw a triangle strip using immediate mode OpenGL, must be passed the argument , which notifies OpenGL a triangle strip is about to be drawn. The family of functions specify the coordinates for each vertex in the triangle strip. For more information, consult The OpenGL Redbook.
To draw the triangle strip in the diagram using immediate mode OpenGL, the code is as follows:
//Vertices below are in Clockwise orientation
//Default setting for glFrontFace is Counter-clockwise
glFrontFace(GL_CW);
glBegin(GL_TRIANGLE_STRIP); glVertex3f( 0.0f, 0.0f, 0.0f ); //vertex 1 glVertex3f( 0.0f, 0.5f, 0.0f ); //vertex 2 glVertex3f( 0.5f, 0.0f, 0.0f ); //vertex 3 glVertex3f( 1.0f, 0.5f, 0.0f ); //vertex 4 glEnd();
Note that only one additional vertex is needed to draw the second triangle. In OpenGL, the order in which the vertices are specified is important so that surface normals are consistent.
Quoting directly from the OpenGL Programming Guide:
GL_TRIANGLE_STRIPDraws a series of triangles (three-sided polygons) using vertices v0, v1, v2, then v2, v1, v3 (note the order), then v2, v3, v4, and so on. The ordering is to ensure that the triangles are all drawn with the same orientation so that the strip can correctly form part of a surface.
It's even clearer within the manual pages:
Draws a connected group of triangles. One triangle is defined for each vertex presented after the first two vertices. For odd , vertices , , and define triangle . For even , vertices , , and define triangle . triangles are drawn.
Note that starts at 1. The above code sample and diagram demonstrate triangles drawn in a clockwise orientation. For those to be considered front-facing, a preceding call to is necessary, which otherwise has an initial value of (meaning that triangles drawn counter-clockwise are front-facing by default). This is significant if and are already active ( by default), because back-facing triangles will be culled, so will not be drawn and will not appear on-screen at all.
Properties and construction
It follows from definition that a subsequence of vertices of a triangle strip also represents a triangle strip. However, if this substrip starts at an even (with 1-based counting) vertex, then the resulting triangles will change their orientation. For example a substrip BCDEF would represent triangles: BCD,CED,DEF.
Similarly, reversal of strips’ vertices will result in the same set of triangles if the strip has an even number of vertices. (e.g. strip FEDCBA will represent the same triangles FED,ECD,DCB,CAB as the original strip). However, if a strip has an odd number of vertices then the reversed strip will represent triangles with opposite orientation. For example, reversal of a strip ABCDE will result in strip EDCBA which represents triangles EDC, DBC, CBA).
Converting a general polygon mesh to a single long strip was until recently generally not possible. Usually the triangle strips are analogous to a set of edge loops, and poles on the model are represented by triangle fans. Tools such as Stripe or FTSG represent the model as several strips. Optimally grouping a set of triangles into sequential strips has been proven NP-complete.