// Static function to find the intersection of two planes
// If they are parallel, returns false and outputs an invalid line struct
// Otherwise, returns true and outputs the line of intersection
public static bool Intersect(Plane a, Plane b, out Line result)
{
Vec3 cross = Vec3.Cross(a.normal, b.normal);
double magsq = cross.ComputeMagnitudeSquared();
if (magsq == 0)
{
// failure! planes did not intersect, or planes were equal
result = new Line { direction = Vec3.Zero, origin = Vec3.Zero }; // not a valid line!
return false;
}
double invmag = 1.0 / Math.Sqrt(magsq);
Vec3 line_direction = cross * invmag;
// using plane a to find intersection (also could try b?)
Vec3 in_a_toward_edge = Vec3.Normalize(Vec3.Cross(a.normal, line_direction));
Vec3 point_in_a = a.normal * a.offset;
double dist = b.PointDistance(point_in_a);
// seems this number could be either the positive or negative of what we want...
double unsigned_r = dist * invmag;
Vec3 positive = point_in_a + in_a_toward_edge * unsigned_r;
Vec3 negative = point_in_a - in_a_toward_edge * unsigned_r;
// figure out which one is actually at the intersection (or closest to it)
double positive_check = new Vec2 { x = a.PointDistance(positive), y = b.PointDistance(positive) }.ComputeMagnitudeSquared();
double negative_check = new Vec2 { x = a.PointDistance(negative), y = b.PointDistance(negative) }.ComputeMagnitudeSquared();
// and use that one as a point on the line (for the out value)
Vec3 point_on_line;
if (positive_check < negative_check)
point_on_line = positive;
else
point_on_line = negative;
// success! planes intersectedx
result = new Line { origin = point_on_line, direction = line_direction };
return true;
}
// Static function to find the intersection of two planes
// If they are parallel, returns false and outputs an invalid line struct
// Otherwise, returns true and outputs the line of intersection
public static bool Intersect(Plane a, Plane b, out Line result)
{
Vec3 cross = Vec3.Cross(a.normal, b.normal);
double magsq = cross.ComputeMagnitudeSquared();
if (magsq == 0)
{
// failure! planes did not intersect, or planes were equal
result = new Line {
direction = Vec3.Zero, origin = Vec3.Zero
}; // not a valid line!
return(false);
}
double invmag = 1.0 / Math.Sqrt(magsq);
Vec3 line_direction = cross * invmag;
// using plane a to find intersection (also could try b?)
Vec3 in_a_toward_edge = Vec3.Normalize(Vec3.Cross(a.normal, line_direction));
Vec3 point_in_a = a.normal * a.offset;
double dist = b.PointDistance(point_in_a);
// seems this number could be either the positive or negative of what we want...
double unsigned_r = dist * invmag;
Vec3 positive = point_in_a + in_a_toward_edge * unsigned_r;
Vec3 negative = point_in_a - in_a_toward_edge * unsigned_r;
// figure out which one is actually at the intersection (or closest to it)
double positive_check = new Vec2 {
x = a.PointDistance(positive), y = b.PointDistance(positive)
}.ComputeMagnitudeSquared();
double negative_check = new Vec2 {
x = a.PointDistance(negative), y = b.PointDistance(negative)
}.ComputeMagnitudeSquared();
// and use that one as a point on the line (for the out value)
Vec3 point_on_line;
if (positive_check < negative_check)
{
point_on_line = positive;
}
else
{
point_on_line = negative;
}
// success! planes intersectedx
result = new Line {
origin = point_on_line, direction = line_direction
};
return(true);
}
public double offset; // Distance from the plane to the origin
#endregion Fields
#region Methods
public static double CheckEquality(Plane a, Plane b)
{
double magprodsq = a.normal.ComputeMagnitudeSquared() * b.normal.ComputeMagnitudeSquared(); // although the magnitude of the normals SHOULD be 1... maybe somebody did something funky
double dot = Vec3.Dot(a.normal, b.normal);
double aparallelness = 1.0 - Math.Sqrt((dot * dot) / magprodsq); // closer to parallel yields smaller values of this
aparallelness *= aparallelness;
double a_from_b = b.PointDistance(a.normal * a.offset);
double b_from_a = a.PointDistance(b.normal * b.offset);
Vec3 a_on_b = a.normal * (a.offset + a_from_b);
Vec3 b_on_a = b.normal * (b.offset + b_from_a);
double distsq1 = (a_on_b - b.normal * b.offset).ComputeMagnitudeSquared(); // coplanar --> same point
double distsq2 = (b_on_a - a.normal * a.offset).ComputeMagnitudeSquared(); // coplanar --> same point
return aparallelness + distsq1 + distsq1;
}
public static double CheckEquality(Plane a, Plane b)
{
double magprodsq = a.normal.ComputeMagnitudeSquared() * b.normal.ComputeMagnitudeSquared(); // although the magnitude of the normals SHOULD be 1... maybe somebody did something funky
double dot = Vec3.Dot(a.normal, b.normal);
double aparallelness = 1.0 - Math.Sqrt((dot * dot) / magprodsq); // closer to parallel yields smaller values of this
aparallelness *= aparallelness;
double a_from_b = b.PointDistance(a.normal * a.offset);
double b_from_a = a.PointDistance(b.normal * b.offset);
Vec3 a_on_b = a.normal * (a.offset + a_from_b);
Vec3 b_on_a = b.normal * (b.offset + b_from_a);
double distsq1 = (a_on_b - b.normal * b.offset).ComputeMagnitudeSquared(); // coplanar --> same point
double distsq2 = (b_on_a - a.normal * a.offset).ComputeMagnitudeSquared(); // coplanar --> same point
return(aparallelness + distsq1 + distsq1);
}
public Vec3 direction; // any nonzero vector along the line
// Checks whether two lines are equal... returns a value, closer to zero = closer to being equal
public static double CheckEquality(Line a, Line b)
{
double magprodsq = a.direction.ComputeMagnitudeSquared() * b.direction.ComputeMagnitudeSquared();
double dot = Vec3.Dot(a.direction, b.direction);
double aparallelness = 1.0 - Math.Sqrt((dot * dot) / magprodsq); // closer to parallel yields smaller values of this
aparallelness *= aparallelness;
Plane plane_a = Plane.FromPositionNormal(a.origin, a.direction);
Plane plane_b = Plane.FromPositionNormal(b.origin, b.direction);
double a_from_b = plane_b.PointDistance(a.origin);
double b_from_a = plane_a.PointDistance(b.origin);
Vec3 a_on_b = a.origin + plane_a.normal * a_from_b;
Vec3 b_on_a = b.origin + plane_b.normal * b_from_a;
double distsq1 = (a_on_b - b.origin).ComputeMagnitudeSquared(); // colinear --> same point
double distsq2 = (b_on_a - a.origin).ComputeMagnitudeSquared(); // colinear --> same point
return(aparallelness + distsq1 + distsq2); // sum of 3 squared quantities... anything big --> big result
}