Geometry and Topology by Jacob Palis, Manfredo DoCarmo

By Jacob Palis, Manfredo DoCarmo

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Plane Geometry and its Groups

San Francisco 1967 Holden-Day. eightvo. , 288pp. , index, hardcover. nice in VG DJ, a number of small closed tears.

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All of the coordinates are squared, then summed. The square root of the result is the length of the n-dimensional vector. 6ot MEL VECTOR To calculate the length of a vector, use the mag command. vector float \$v\$1ength -- mag( \$v )- If you need to calculate the length of a 2D vector, the hyp0t command can be used. 4, \$1ength = h y p o t ( print \$1ength. y ). 188449 FLOAT A R R A Y To calculate the length of a vector as a float array, use the following procedure. proc f l o a t len( { return sqrt( float \$v[] \$v[O]*\$v[O] ) + \$v[1]*\$v[1] + \$v[2]*\$v[2] } The following is an example of use of this procedure.

The length of vector c is simply the dot product of the vectors a and b. fi)b DISTANCE TO LINE This same method can be used to calculate the perpendicular distance from a point p to a line, running through the points p0 and p l . 6, the length of vector d is the distance from the vector a to its projection on the vector b. The vector a is calculated as follows. a=p-pO Vector b is used to represent the line. It is normalized to ensure that it has a unit length. b=pl-pO b = normalize(p1 - pO) As shown previously, the vector c is A A c = (a-b)b The vector d is d--ame = a- A A (a.

5, // Initialized as ( 4 . 2) Although the vector data type is convenient for performing vector operations, many of Maya's MEL commands and procedures don't support vector operations. For instance, a quite common task is getting the position of a transform. 0 onward, it is valid to explicitly assign this array of three scalars to a vector as follows. translate'. In earlier versions of Maya, this would have caused an error. In all versions it isn't possible to directly assign a vector to an attribute.