# Algebra - Math -Counterclockwise

Hello ,

how can I now (thro some formula) the order of vertex to be sure I’m render them
counterclockwise.

I mean :

Triangle_1:
v1= - 15,0,0
v2=0,-15,0
v3=15,0,0
Triangle_2:
v1= - 15,0,0
v2=0,15,0
v3=15,0,0

is there any formula that can tell me form which vertex to start and from which to and
so I can be sure about counterclockwise ???

A triangle with right handed orientation must be “oriented” to something. A soccer ball is a good example. The polygons on the surface should have their vertices ordered so that the outward pointing normal is away from the centroid. Using your right hand, the sequence of points swept by your first finger in order (1->2->3->etc.) should leave your thumb outside the soccer ball. Graphics hardware uses vertex sequencing to figure out if the polygon is inside or outside a mesh.

…1…
…/—…
…/-----…
…/-------…
…/---------…
…2-----------3…
is outward pointing with respect to your monitor. (This assumes a flat screen has some volume too.)

If you’re really hard core, right handed is defined in group theory and used in theoretical physics. e1 op e2 yields +e3 in a right handed system and –e3 for a left one. The operator op is typically the cross product. In 3D space, there exist three + permutations {xyz,zxy,yzx} and three negative permutations {yxz,zyx,xzy}. This is important for rigid body mechanics and computer graphics because matrix operations that don’t preserve handededness (i.e. that have –1 for eigenvalues of orthonormal matrices) actually invert an object akin to pulling a sock inside out. Thus translational, rotational, and scaling transforms have eigenvalues of 1. Other types may or may not satisfy this property.

[This message has been edited by iss (edited 05-18-2001).]