Blaine Hodge's Homepage home: http://www.geocities.com/SiliconValley/Code/1219/ e-mail: craterz@hotmail.com Addition & Subtraction a + b = ( a.x + b.x, a.y + b.y, a.z + b.z ) a - b = ( a.x - b.x, a.y - b.y, a.z - b.z ) -a = ( -a.x, -a.y, -a.z ) a - b = a + -b Scaling s * a = a * s = ( a.x * s, a.y * s, a.z * s ) a / s = a * (1/s) = ( a.x / s, a.y / s, a.z / s ) Length & Distance length( a ) = sqrt( a.x * a.x + a.y * a.y + a.z * a.z ) distance( a, b ) = length( a - b ) Unit Vector normalize( a ) = a * (1 / len( a )) = a / len( a ) Dot Product (Scalar) dot( a, b ) = a.x * b.x + a.y * b.y + a.z * b.z dot( a, b ) = len( a ) * len( b ) * cos(ø) Cross Product (Vector) cross( a, b ) = ( a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x ) len( cross( a, b ) ) = len( a ) * len( b ) * sin( theta ) Plane Equation dot( n, p ) + k = 0 dot( n, p ) + k > 0 // in front of the plane dot( n, p ) + k = 0 // lies on the plane dot( n, p ) + k < 0 // in behind the plane Plane from 3 Points n = normalize( cross( p3 - p2, p1 - p2 ) ) k = dot( n, p1 ) [ powered by Latte and Python | last updated Sat Aug 25 00:54:56 2001 PST ]