public static class Line
{
public float a;
public float b;
public float c;Line in 2D cartesian spacecan be defined implicitly by equation
ax + by + c = 0.
Such implicit definition is associated with a line coordinate system. Every plane point (x, y) be uniquely represented in the line’s (s, t) coordinates as follows:
(x, y) = O + sT + tN,
where O is the origin of the coordinate system and is defined as the projection of cartesian origin (0, 0) onto the line, whereas, T = (-b, a) and N = (a, b) are the tangent and normal vectors of the line.
Note: Different implicit definitions of the same line may yield different coordinate systems.
Represents an implicit line definition and provides routines to work with its coordinate system
public static class Line
{
public float a;
public float b;
public float c;Creates line with given coefficients
public Line(float a, float b, float c) {
this.a = a;
this.b = b;
this.c = c;
}Gets the line origin defined as the projection of the (0, 0) cartesian point onto the line. This is the origin of this line’s coordinate system.
public PVector origin() {
float c1 = -c / (a * a + b * b);
return new PVector(a * c1, b * c1);
}Gets the (-b, a) vector. This is the base vector for the s line
coordinate.
public PVector tangent() {
return new PVector(-b, a);
}Gets the (a, b) vector. This is the base vector for the t line
coordinate.
public PVector normal() {
return new PVector(a, b);
}Converts point from (x, y) cartesian coordinates to (s, t) line coordinates
public LVector map(PVector p) {
float c1 = a * a + b * b;
float t = (a * p.x + b * p.y + c) / c1;
float c2 = c / c1 - t;
float s = abs(a) > abs(b) ? (p.y + b * c2) / a : -(p.x + a * c2) / b;
return new LVector(s, t);
}Converts point from (s, t) line coordinates to cartesian (x, y) coordinates
public PVector unmap(LVector l) {
return unmap(l.s, l.t);
}Converts point from (s, t) line coordinates to cartesian (x, y) coordinates
public PVector unmap(float s, float t) {
final float c1 = t - c / (a * a + b * b);
return new PVector(c1 * a - s * b, c1 * b + s * a);
}Converts point given in this line’s coordinates to the coordinate system of another line
public LVector remap(Line other, LVector l) {
return remap(other, l.s, l.t);
}Converts point given in this line’s coordinates to the coordinate system of another line
public LVector remap(Line other, float s, float t) {
return map(other.unmap(s, t));
}
}Represents a point in line (s, t) coordinates
public static class LVector
{
public float s;
public float t;Creates new point with given coordinates
public LVector(float s, float t) {
this.s = s;
this.t = t;
}
}