/**
* Project the value given along the line segment, where 0 represents A and 1 represents B.
* Tolerance is used to snap points to A or B if close enough. If u < 0 return A and if u > 1
* return B and the point is beyond the tolerance, return null
*
* @param u
* @param tolerance tolerance for snapping to end points
* @param target target vector
* @throws IllegalArgumentException if u was infinite or NaN
* @throws NullPointerException if tolerance or target was null
*/
public void projectClosest(double u, Tolerance tolerance, VectBuilder target)
throws NullPointerException, IllegalArgumentException {
double x = (u * (bx - ax)) + ax;
double y = (u * (by - ay)) + ay;
if ((u < 0) || tolerance.match(x, y, ax, ay)) {
getA(target);
} else if ((u > 1) || tolerance.match(x, y, bx, by)) {
getB(target);
} else {
target.set(x, y);
}
}
static void intersectionLineCircleInternal(
double ax,
double ay,
double bx,
double by,
double cx,
double cy,
double radius,
Tolerance tolerance,
VectBuilder working,
VectList intersections) {
projectOnToLineInternal(
ax, ay, bx, by, cx, cy, tolerance,
working); // get the closest point on the line to the circle center
double dx = working.getX();
double dy = working.getY();
double distToLineSq = Vect.distSq(cx, cy, dx, dy);
double radiusSq = radius * radius;
switch (tolerance.check(distToLineSq - radiusSq)) {
case 1: // dist to line is greater than radius - line does not intersect circle
return;
case 0: // dist to line matches radius - line touches circle
intersections.add(dx, dy);
return;
default: // dist to line is less than radius - line crosses circle
double mx = bx - ax;
double my = by - ay;
double segmentLen = Math.sqrt(mx * mx + my * my);
double projectDist;
if (tolerance.check(distToLineSq) == 0) { // line crosses circle center
projectDist = radius;
dx = cx;
dy = cy;
} else {
projectDist = Math.sqrt(radiusSq - distToLineSq);
}
double mul = projectDist / segmentLen;
mx *= mul;
my *= mul;
intersections.add(dx - mx, dy - my);
intersections.add(dx + mx, dy + my);
}
}
static boolean project(
double ax,
double ay,
double bx,
double by,
double u,
Tolerance tolerance,
VectBuilder target) {
double x = (u * (bx - ax)) + ax;
double y = (u * (by - ay)) + ay;
if (tolerance.match(x, y, ax, ay)) {
target.set(ax, ay);
return true;
} else if (tolerance.match(x, y, bx, by)) {
target.set(bx, by);
return true;
} else {
target.set(x, y);
return ((u > 0) && (u < 1));
}
}
/**
* Determine if segments intersect. Segments which do not intersect, but are within the tolerance
* given from each other are considered to intersect unless they are parallel
*
* @param line
* @param tolerance
* @return true if segments intersect, false otherwise
* @throws NullPointerException if line or tolerance was null
*/
public boolean intersectsSeg(Line line, Tolerance tolerance) throws NullPointerException {
double jax = line.ax;
double jay = line.ay;
double jbx = line.bx;
double jby = line.by;
double denom = getDenom(ax, ay, bx, by, jax, jay, jbx, jby);
if (denom == 0.0) { // Lines are parallel.
return false;
}
double ui =
((jbx - jax) * (ay - jay) - (jby - jay) * (ax - jax))
/ denom; // projected distance along i and j
double uj = ((bx - ax) * (ay - jay) - (by - ay) * (ax - jax)) / denom;
if ((ui >= 0) && (ui <= 1) && (uj >= 0) && (uj <= 1)) {
return true;
}
double x = (ui * (bx - ax)) + ax;
double y = (ui * (by - ay)) + ay;
if (ui < 0) {
if (!tolerance.match(x, y, ax, ay)) {
return false;
}
} else if (ui > 1) {
if (!tolerance.match(x, y, bx, by)) {
return false;
}
}
if (uj < 0) {
if (!tolerance.match(x, y, jax, jay)) {
return false;
}
} else if (uj > 1) {
if (!tolerance.match(x, y, jbx, jby)) {
return false;
}
}
return true;
}
/**
* Determine if the point given lies to the left, right, or on the line given.
*
* @param ax
* @param ay
* @param bx
* @param by
* @param x
* @param y
* @param accuracy
* @return 1 if left of line, -1 if right of line, 0 if on line.
*/
public static int counterClockwise(
double ax, double ay, double bx, double by, double x, double y, Tolerance accuracy) {
bx -= ax;
by -= ay;
x -= ax;
y -= ay;
double ccw = x * by - y * bx;
if (ccw
== 0.0) { // Point is colinear - classify based on whether b is further away from a than
// point
ccw = ((x * x) + (y * y)) - ((bx * bx) + (by * by));
ccw = Math.max(ccw, 0);
}
return accuracy.check(ccw);
}
static boolean intersectionSegInternal(
double ax,
double ay,
double bx,
double by,
double jax,
double jay,
double jbx,
double jby,
Tolerance tolerance,
VectBuilder target)
throws NullPointerException {
if (Vect.compare(ax, ay, bx, by) > 0) {
double tmp = ax;
ax = bx;
bx = tmp;
tmp = ay;
ay = by;
by = tmp;
}
if (Vect.compare(jax, jay, jbx, jby) > 0) {
double tmp = jax;
jax = jbx;
jbx = tmp;
tmp = jay;
jay = jby;
jby = tmp;
}
if (compare(ax, ay, bx, by, jax, jay, jbx, jby) > 0) {
double tmp = ax;
ax = jax;
jax = tmp;
tmp = ay;
ay = jay;
jay = tmp;
tmp = bx;
bx = jbx;
jbx = tmp;
tmp = by;
by = jby;
jby = tmp;
}
double denom = getDenom(ax, ay, bx, by, jax, jay, jbx, jby);
if (denom == 0.0) { // Lines are parallel.
return false;
}
double ui =
((jbx - jax) * (ay - jay) - (jby - jay) * (ax - jax))
/ denom; // projected distance along i and j
double uj = ((bx - ax) * (ay - jay) - (by - ay) * (ax - jax)) / denom;
double x, y;
if (ax == bx) {
x = ax;
} else if (jax == jbx) {
x = jax;
} else {
x = (ui * (bx - ax)) + ax;
}
if (ay == by) {
y = ay;
} else if (jay == jby) {
y = jay;
} else {
y = (ui * (by - ay)) + ay;
}
boolean ia = tolerance.match(x, y, ax, ay);
boolean ib = tolerance.match(x, y, bx, by);
boolean i = ia || ib || ((ui >= 0) && (ui <= 1));
boolean ja = tolerance.match(x, y, jax, jay);
boolean jb = tolerance.match(x, y, jbx, jby);
boolean j = ja || jb || ((uj >= 0) && (uj <= 1));
if (i && j) {
if (ia) {
target.set(ax, ay);
} else if (ib) {
target.set(bx, by);
} else if (ja) {
target.set(jax, jay);
} else if (jb) {
target.set(jbx, jby);
} else {
target.set(x, y);
}
return true;
}
return false;
}
/**
* Determine if this line is parallell to that given, with differences in slope within the
* tolerance
*
* @param line
* @param tolerance
* @return
* @throws NullPointerException if line or tolerance was null
*/
public boolean isParallel(Line line, Tolerance tolerance) throws NullPointerException {
double denom = getDenom(ax, ay, bx, by, line.ax, line.ay, line.bx, line.by);
return tolerance.match(denom, 0);
}
/**
* Get the side of the line on which vect lies. Positive values imply that it lies on the left of
* the line. Negative values imply it lies on the right of the line. 0 implies it lies on the line
*
* @param vect
* @param tolerance
* @return
* @throws IllegalStateException if invalid
*/
public int sign(Vect vect, Tolerance tolerance) throws NullPointerException {
return tolerance.check(sign(vect));
}
/**
* Determine if the distance between the end points is greater than the tolerance given
*
* @param tolerance
* @return true if distance is greater, false otherwise
*/
public boolean isValid(Tolerance tolerance) {
return (!tolerance.match(ax, ay, bx, by));
}