Processing: Creative Coding and Computational Art

Normalizing a vector
When working with vectors, it is common practice to find this base ratio of a vector, which
is referred to as normalizing a vector. Normalizing simply means reducing the magnitude
(length) of a vector to 1, which is done by dividing each component of a vector by its overall
length. For example if you have vector v, you can find its length like this (expressed in
code):
length = sqrt(v.x*v.x + v.y*v.y);
Then to find the base ratio, you simply divide each of the vector’s components by its
length:
normalizedVector.x = v.x / length;
normalizedVector.y = v.y / length;
Again, this base ratio, or normalized vector, expresses the direction of the vector. For
example, if we have a line and we want to animate an ellipse at a certain speed along the
line, we can treat the line as a vector. Once we have the length of the line, we can normalize
it and use the normalized values as the direction for the ellipse to travel, which we
can then multiply by any speed we choose. Here’s a sketch that does precisely this (shown
in Figure 11-16):
// Moving Along a Vector
float lineX1, lineY1, lineX2, lineY2;
float vectX, vectY, vectMag, directionX, directionY;
float ellipseX, ellipseY;
float ellipseSpeed = 2;
void setup(){
size(400, 400);
fill(128);
smooth();
lineX1 = 100;
lineY1 = 75;
lineX2 = 300;
lineY2 = 325;
// express line as a vector
vectX = lineX2-lineX1;
vectY = lineY2-lineY1;
// find magnitude(length) of vector
vectMag = sqrt(vectX*vectX + vectY*vectY);
/* normalize vector to get
base direction ratio */
directionX = vectX/vectMag;
directionY = vectY/vectMag;
MOTION
523
11