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LUCENE-7241: More performance improvements

This commit is contained in:
Karl Wright 2016-05-05 16:16:55 -04:00
parent 7917fd8ff3
commit 88f70ac214
1 changed files with 150 additions and 1 deletions
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151
lucene/spatial3d/src/java/org/apache/lucene/spatial3d/geom/Plane.java
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@ -1746,7 +1746,156 @@ public class Plane extends Vector {
//System.err.println(" no notable points inside found; no intersection");
return false;
}
return findIntersections(planetModel, q, bounds, moreBounds).length > 0;
// Save on allocations; do inline instead of calling findIntersections
//System.err.println("Looking for intersection between plane "+this+" and plane "+q+" within bounds");
// Unnormalized, unchecked...
final Vector lineVector = new Vector(y * q.z - z * q.y, z * q.x - x * q.z, x * q.y - y * q.x);
if (Math.abs(lineVector.x) < MINIMUM_RESOLUTION && Math.abs(lineVector.y) < MINIMUM_RESOLUTION && Math.abs(lineVector.z) < MINIMUM_RESOLUTION) {
// Degenerate case: parallel planes
//System.err.println(" planes are parallel - no intersection");
return false;
}
// The line will have the equation: A t + A0 = x, B t + B0 = y, C t + C0 = z.
// We have A, B, and C. In order to come up with A0, B0, and C0, we need to find a point that is on both planes.
// To do this, we find the largest vector value (either x, y, or z), and look for a point that solves both plane equations
// simultaneous. For example, let's say that the vector is (0.5,0.5,1), and the two plane equations are:
// 0.7 x + 0.3 y + 0.1 z + 0.0 = 0
// and
// 0.9 x - 0.1 y + 0.2 z + 4.0 = 0
// Then we'd pick z = 0, so the equations to solve for x and y would be:
// 0.7 x + 0.3y = 0.0
// 0.9 x - 0.1y = -4.0
// ... which can readily be solved using standard linear algebra. Generally:
// Q0 x + R0 y = S0
// Q1 x + R1 y = S1
// ... can be solved by Cramer's rule:
// x = det(S0 R0 / S1 R1) / det(Q0 R0 / Q1 R1)
// y = det(Q0 S0 / Q1 S1) / det(Q0 R0 / Q1 R1)
// ... where det( a b / c d ) = ad - bc, so:
// x = (S0 * R1 - R0 * S1) / (Q0 * R1 - R0 * Q1)
// y = (Q0 * S1 - S0 * Q1) / (Q0 * R1 - R0 * Q1)
double x0;
double y0;
double z0;
// We try to maximize the determinant in the denominator
final double denomYZ = this.y * q.z - this.z * q.y;
final double denomXZ = this.x * q.z - this.z * q.x;
final double denomXY = this.x * q.y - this.y * q.x;
if (Math.abs(denomYZ) >= Math.abs(denomXZ) && Math.abs(denomYZ) >= Math.abs(denomXY)) {
// X is the biggest, so our point will have x0 = 0.0
if (Math.abs(denomYZ) < MINIMUM_RESOLUTION_SQUARED) {
//System.err.println(" Denominator is zero: no intersection");
return false;
}
final double denom = 1.0 / denomYZ;
x0 = 0.0;
y0 = (-this.D * q.z - this.z * -q.D) * denom;
z0 = (this.y * -q.D + this.D * q.y) * denom;
} else if (Math.abs(denomXZ) >= Math.abs(denomXY) && Math.abs(denomXZ) >= Math.abs(denomYZ)) {
// Y is the biggest, so y0 = 0.0
if (Math.abs(denomXZ) < MINIMUM_RESOLUTION_SQUARED) {
//System.err.println(" Denominator is zero: no intersection");
return false;
}
final double denom = 1.0 / denomXZ;
x0 = (-this.D * q.z - this.z * -q.D) * denom;
y0 = 0.0;
z0 = (this.x * -q.D + this.D * q.x) * denom;
} else {
// Z is the biggest, so Z0 = 0.0
if (Math.abs(denomXY) < MINIMUM_RESOLUTION_SQUARED) {
//System.err.println(" Denominator is zero: no intersection");
return false;
}
final double denom = 1.0 / denomXY;
x0 = (-this.D * q.y - this.y * -q.D) * denom;
y0 = (this.x * -q.D + this.D * q.x) * denom;
z0 = 0.0;
}
// Once an intersecting line is determined, the next step is to intersect that line with the ellipsoid, which
// will yield zero, one, or two points.
// The ellipsoid equation: 1,0 = x^2/a^2 + y^2/b^2 + z^2/c^2
// 1.0 = (At+A0)^2/a^2 + (Bt+B0)^2/b^2 + (Ct+C0)^2/c^2
// A^2 t^2 / a^2 + 2AA0t / a^2 + A0^2 / a^2 + B^2 t^2 / b^2 + 2BB0t / b^2 + B0^2 / b^2 + C^2 t^2 / c^2 + 2CC0t / c^2 + C0^2 / c^2 - 1,0 = 0.0
// [A^2 / a^2 + B^2 / b^2 + C^2 / c^2] t^2 + [2AA0 / a^2 + 2BB0 / b^2 + 2CC0 / c^2] t + [A0^2 / a^2 + B0^2 / b^2 + C0^2 / c^2 - 1,0] = 0.0
// Use the quadratic formula to determine t values and candidate point(s)
final double A = lineVector.x * lineVector.x * planetModel.inverseAbSquared +
lineVector.y * lineVector.y * planetModel.inverseAbSquared +
lineVector.z * lineVector.z * planetModel.inverseCSquared;
final double B = 2.0 * (lineVector.x * x0 * planetModel.inverseAbSquared + lineVector.y * y0 * planetModel.inverseAbSquared + lineVector.z * z0 * planetModel.inverseCSquared);
final double C = x0 * x0 * planetModel.inverseAbSquared + y0 * y0 * planetModel.inverseAbSquared + z0 * z0 * planetModel.inverseCSquared - 1.0;
final double BsquaredMinus = B * B - 4.0 * A * C;
if (Math.abs(BsquaredMinus) < MINIMUM_RESOLUTION_SQUARED) {
//System.err.println(" One point of intersection");
final double inverse2A = 1.0 / (2.0 * A);
// One solution only
final double t = -B * inverse2A;
// Maybe we can save ourselves the cost of construction of a point?
final double pointX = lineVector.x * t + x0;
final double pointY = lineVector.y * t + y0;
final double pointZ = lineVector.z * t + z0;
for (final Membership bound : bounds) {
if (!bound.isWithin(pointX, pointY, pointZ)) {
return false;
}
}
for (final Membership bound : moreBounds) {
if (!bound.isWithin(pointX, pointY, pointZ)) {
return false;
}
}
return true;
} else if (BsquaredMinus > 0.0) {
//System.err.println(" Two points of intersection");
final double inverse2A = 1.0 / (2.0 * A);
// Two solutions
final double sqrtTerm = Math.sqrt(BsquaredMinus);
final double t1 = (-B + sqrtTerm) * inverse2A;
final double t2 = (-B - sqrtTerm) * inverse2A;
// Up to two points being returned. Do what we can to save on object creation though.
final double point1X = lineVector.x * t1 + x0;
final double point1Y = lineVector.y * t1 + y0;
final double point1Z = lineVector.z * t1 + z0;
boolean point1Valid = true;
for (final Membership bound : bounds) {
if (!bound.isWithin(point1X, point1Y, point1Z)) {
point1Valid = false;
break;
}
}
if (point1Valid) {
for (final Membership bound : moreBounds) {
if (!bound.isWithin(point1X, point1Y, point1Z)) {
point1Valid = false;
break;
}
}
}
if (point1Valid) {
return true;
}
final double point2X = lineVector.x * t2 + x0;
final double point2Y = lineVector.y * t2 + y0;
final double point2Z = lineVector.z * t2 + z0;
for (final Membership bound : bounds) {
if (!bound.isWithin(point2X, point2Y, point2Z)) {
return false;
}
}
for (final Membership bound : moreBounds) {
if (!bound.isWithin(point2X, point2Y, point2Z)) {
return false;
}
}
return true;
} else {
//System.err.println(" no solutions - no intersection");
return false;
}
}
/**