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use crate::math::{Point, Real, Vector};
use crate::query::{PointProjection, PointQuery, PointQueryWithLocation};
use crate::shape::{FeatureId, Tetrahedron, TetrahedronPointLocation};
impl PointQuery for Tetrahedron {
#[inline]
fn project_local_point(&self, pt: &Point<Real>, solid: bool) -> PointProjection {
self.project_local_point_and_get_location(pt, solid).0
}
#[inline]
fn project_local_point_and_get_feature(
&self,
pt: &Point<Real>,
) -> (PointProjection, FeatureId) {
let (proj, loc) = self.project_local_point_and_get_location(pt, false);
let feature = match loc {
TetrahedronPointLocation::OnVertex(i) => FeatureId::Vertex(i),
TetrahedronPointLocation::OnEdge(i, _) => FeatureId::Edge(i),
TetrahedronPointLocation::OnFace(i, _) => FeatureId::Face(i),
TetrahedronPointLocation::OnSolid => unreachable!(),
};
(proj, feature)
}
}
impl PointQueryWithLocation for Tetrahedron {
type Location = TetrahedronPointLocation;
#[inline]
fn project_local_point_and_get_location(
&self,
pt: &Point<Real>,
solid: bool,
) -> (PointProjection, Self::Location) {
let ab = self.b - self.a;
let ac = self.c - self.a;
let ad = self.d - self.a;
let ap = pt - self.a;
/*
* Voronoï regions of vertices.
*/
let ap_ab = ap.dot(&ab);
let ap_ac = ap.dot(&ac);
let ap_ad = ap.dot(&ad);
if ap_ab <= 0.0 && ap_ac <= 0.0 && ap_ad <= 0.0 {
// Voronoï region of `a`.
let proj = PointProjection::new(false, self.a);
return (proj, TetrahedronPointLocation::OnVertex(0));
}
let bc = self.c - self.b;
let bd = self.d - self.b;
let bp = pt - self.b;
let bp_bc = bp.dot(&bc);
let bp_bd = bp.dot(&bd);
let bp_ab = bp.dot(&ab);
if bp_bc <= 0.0 && bp_bd <= 0.0 && bp_ab >= 0.0 {
// Voronoï region of `b`.
let proj = PointProjection::new(false, self.b);
return (proj, TetrahedronPointLocation::OnVertex(1));
}
let cd = self.d - self.c;
let cp = pt - self.c;
let cp_ac = cp.dot(&ac);
let cp_bc = cp.dot(&bc);
let cp_cd = cp.dot(&cd);
if cp_cd <= 0.0 && cp_bc >= 0.0 && cp_ac >= 0.0 {
// Voronoï region of `c`.
let proj = PointProjection::new(false, self.c);
return (proj, TetrahedronPointLocation::OnVertex(2));
}
let dp = pt - self.d;
let dp_cd = dp.dot(&cd);
let dp_bd = dp.dot(&bd);
let dp_ad = dp.dot(&ad);
if dp_ad >= 0.0 && dp_bd >= 0.0 && dp_cd >= 0.0 {
// Voronoï region of `d`.
let proj = PointProjection::new(false, self.d);
return (proj, TetrahedronPointLocation::OnVertex(3));
}
/*
* Voronoï regions of edges.
*/
#[inline(always)]
fn check_edge(
i: usize,
a: &Point<Real>,
_: &Point<Real>,
nabc: &Vector<Real>,
nabd: &Vector<Real>,
ap: &Vector<Real>,
ab: &Vector<Real>,
ap_ab: Real, /*ap_ac: Real, ap_ad: Real,*/
bp_ab: Real, /*bp_ac: Real, bp_ad: Real*/
) -> (
Real,
Real,
Option<(PointProjection, TetrahedronPointLocation)>,
) {
let ab_ab = ap_ab - bp_ab;
// NOTE: The following avoids the subsequent cross and dot products but are not
// numerically stable.
//
// let dabc = ap_ab * (ap_ac - bp_ac) - ap_ac * ab_ab;
// let dabd = ap_ab * (ap_ad - bp_ad) - ap_ad * ab_ab;
let ap_x_ab = ap.cross(ab);
let dabc = ap_x_ab.dot(nabc);
let dabd = ap_x_ab.dot(nabd);
// TODO: the case where ab_ab == 0.0 is not well defined.
if ab_ab != 0.0 && dabc >= 0.0 && dabd >= 0.0 && ap_ab >= 0.0 && ap_ab <= ab_ab {
// Voronoi region of `ab`.
let u = ap_ab / ab_ab;
let bcoords = [1.0 - u, u];
let res = a + ab * u;
let proj = PointProjection::new(false, res);
(
dabc,
dabd,
Some((proj, TetrahedronPointLocation::OnEdge(i as u32, bcoords))),
)
} else {
(dabc, dabd, None)
}
}
// Voronoï region of ab.
// let bp_ad = bp_bd + bp_ab;
// let bp_ac = bp_bc + bp_ab;
let nabc = ab.cross(&ac);
let nabd = ab.cross(&ad);
let (dabc, dabd, res) = check_edge(
0, &self.a, &self.b, &nabc, &nabd, &ap, &ab, ap_ab,
/*ap_ac, ap_ad,*/ bp_ab, /*, bp_ac, bp_ad*/
);
if let Some(res) = res {
return res;
}
// Voronoï region of ac.
// Substitutions (wrt. ab):
// b -> c
// c -> d
// d -> b
// let cp_ab = cp_ac - cp_bc;
// let cp_ad = cp_cd + cp_ac;
let nacd = ac.cross(&ad);
let (dacd, dacb, res) = check_edge(
1, &self.a, &self.c, &nacd, &-nabc, &ap, &ac, ap_ac,
/*ap_ad, ap_ab,*/ cp_ac, /*, cp_ad, cp_ab*/
);
if let Some(res) = res {
return res;
}
// Voronoï region of ad.
// Substitutions (wrt. ab):
// b -> d
// c -> b
// d -> c
// let dp_ac = dp_ad - dp_cd;
// let dp_ab = dp_ad - dp_bd;
let (dadb, dadc, res) = check_edge(
2, &self.a, &self.d, &-nabd, &-nacd, &ap, &ad, ap_ad,
/*ap_ab, ap_ac,*/ dp_ad, /*, dp_ab, dp_ac*/
);
if let Some(res) = res {
return res;
}
// Voronoï region of bc.
// Substitutions (wrt. ab):
// a -> b
// b -> c
// c -> a
// let cp_bd = cp_cd + cp_bc;
let nbcd = bc.cross(&bd);
// NOTE: nabc = nbcd
let (dbca, dbcd, res) = check_edge(
3, &self.b, &self.c, &nabc, &nbcd, &bp, &bc, bp_bc,
/*-bp_ab, bp_bd,*/ cp_bc, /*, -cp_ab, cp_bd*/
);
if let Some(res) = res {
return res;
}
// Voronoï region of bd.
// Substitutions (wrt. ab):
// a -> b
// b -> d
// d -> a
// let dp_bc = dp_bd - dp_cd;
// NOTE: nbdc = -nbcd
// NOTE: nbda = nabd
let (dbdc, dbda, res) = check_edge(
4, &self.b, &self.d, &-nbcd, &nabd, &bp, &bd, bp_bd,
/*bp_bc, -bp_ab,*/ dp_bd, /*, dp_bc, -dp_ab*/
);
if let Some(res) = res {
return res;
}
// Voronoï region of cd.
// Substitutions (wrt. ab):
// a -> c
// b -> d
// c -> a
// d -> b
// NOTE: ncda = nacd
// NOTE: ncdb = nbcd
let (dcda, dcdb, res) = check_edge(
5, &self.c, &self.d, &nacd, &nbcd, &cp, &cd, cp_cd,
/*-cp_ac, -cp_bc,*/ dp_cd, /*, -dp_ac, -dp_bc*/
);
if let Some(res) = res {
return res;
}
/*
* Voronoï regions of faces.
*/
#[inline(always)]
fn check_face(
i: usize,
a: &Point<Real>,
b: &Point<Real>,
c: &Point<Real>,
ap: &Vector<Real>,
bp: &Vector<Real>,
cp: &Vector<Real>,
ab: &Vector<Real>,
ac: &Vector<Real>,
ad: &Vector<Real>,
dabc: Real,
dbca: Real,
dacb: Real,
/* ap_ab: Real, bp_ab: Real, cp_ab: Real,
ap_ac: Real, bp_ac: Real, cp_ac: Real, */
) -> Option<(PointProjection, TetrahedronPointLocation)> {
if dabc < 0.0 && dbca < 0.0 && dacb < 0.0 {
let n = ab.cross(ac); // TODO: is is possible to avoid this cross product?
if n.dot(ad) * n.dot(ap) < 0.0 {
// Voronoï region of the face.
// NOTE:
// The following avoids expansive computations but are not very
// numerically stable.
//
// let va = bp_ab * cp_ac - cp_ab * bp_ac;
// let vb = cp_ab * ap_ac - ap_ab * cp_ac;
// let vc = ap_ab * bp_ac - bp_ab * ap_ac;
// NOTE: the normalization may fail even if the dot products
// above were < 0. This happens, e.g., when we use fixed-point
// numbers and there are not enough decimal bits to perform
// the normalization.
let normal = n.try_normalize(crate::math::DEFAULT_EPSILON)?;
let vc = normal.dot(&ap.cross(bp));
let va = normal.dot(&bp.cross(cp));
let vb = normal.dot(&cp.cross(ap));
let denom = va + vb + vc;
assert!(denom != 0.0);
let inv_denom = 1.0 / denom;
let bcoords = [va * inv_denom, vb * inv_denom, vc * inv_denom];
let res = a * bcoords[0] + b.coords * bcoords[1] + c.coords * bcoords[2];
let proj = PointProjection::new(false, res);
return Some((proj, TetrahedronPointLocation::OnFace(i as u32, bcoords)));
}
}
None
}
// Face abc.
if let Some(res) = check_face(
0, &self.a, &self.b, &self.c, &ap, &bp, &cp, &ab, &ac, &ad, dabc, dbca,
dacb,
/*ap_ab, bp_ab, cp_ab,
ap_ac, bp_ac, cp_ac*/
) {
return res;
}
// Face abd.
if let Some(res) = check_face(
1, &self.a, &self.b, &self.d, &ap, &bp, &dp, &ab, &ad, &ac, dadb, dabd,
dbda,
/*ap_ab, bp_ab, dp_ab,
ap_ad, bp_ad, dp_ad*/
) {
return res;
}
// Face acd.
if let Some(res) = check_face(
2, &self.a, &self.c, &self.d, &ap, &cp, &dp, &ac, &ad, &ab, dacd, dcda,
dadc,
/*ap_ac, cp_ac, dp_ac,
ap_ad, cp_ad, dp_ad*/
) {
return res;
}
// Face bcd.
if let Some(res) = check_face(
3, &self.b, &self.c, &self.d, &bp, &cp, &dp, &bc, &bd, &-ab, dbcd, dcdb,
dbdc,
/*bp_bc, cp_bc, dp_bc,
bp_bd, cp_bd, dp_bd*/
) {
return res;
}
if !solid {
// XXX: implement the non-solid projection.
unimplemented!(
"Non-solid ray-cast/point projection on a tetrahedron is not yet implemented."
)
}
let proj = PointProjection::new(true, *pt);
(proj, TetrahedronPointLocation::OnSolid)
}
}