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Return barycentric coordinates for rish point projection on triangles. #152

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Return barycentric coordinates for rish point projection on triangles. #152

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6 changes: 2 additions & 4 deletions ncollide_geometry/query/point_internal/point_mesh.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -13,8 +13,7 @@ impl<P, M, I, E> PointQuery<P, M> for BaseMesh<P, I, E>
E: BaseMeshElement<I, P> + PointQuery<P, Id> + RichPointQuery<P, Id> {
#[inline]
fn project_point(&self, m: &M, point: &P, solid: bool) -> PointProjection<P> {
let (projection, _) = self.project_point_with_extra_info(m, point, solid);
projection
self.project_point_with_extra_info(m, point, solid).0
}

#[inline]
Expand Down Expand Up @@ -152,8 +151,7 @@ impl<P: Point, M: Isometry<P>> PointQuery<P, M> for TriMesh<P> {
impl<P: Point, M: Isometry<P>> PointQuery<P, M> for Polyline<P> {
#[inline]
fn project_point(&self, m: &M, point: &P, solid: bool) -> PointProjection<P> {
let (projection, _) = self.project_point_with_extra_info(m, point, solid);
projection
self.project_point_with_extra_info(m, point, solid).0
}

#[inline]
Expand Down
3 changes: 1 addition & 2 deletions ncollide_geometry/query/point_internal/point_query.rs
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Expand Up @@ -11,6 +11,7 @@ pub struct PointProjection<P: Point> {

impl<P: Point> PointProjection<P> {
/// Initializes a new `PointProjection`.
#[inline]
pub fn new(is_inside: bool, point: P) -> PointProjection<P> {
PointProjection {
is_inside: is_inside,
Expand All @@ -22,7 +23,6 @@ impl<P: Point> PointProjection<P> {
/// Trait of objects that can be tested for point inclusion and projection.
pub trait PointQuery<P: Point, M> {
/// Projects a point on `self` transformed by `m`.
#[inline]
fn project_point(&self, m: &M, pt: &P, solid: bool) -> PointProjection<P>;

/// Computes the minimal distance between a point and `self` transformed by `m`.
Expand Down Expand Up @@ -70,7 +70,6 @@ pub trait RichPointQuery<P: Point, M> {
type ExtraInfo;

/// Projects a point on `self` transformed by `m`.
#[inline]
fn project_point_with_extra_info(&self, m: &M, pt: &P, solid: bool)
-> (PointProjection<P>, Self::ExtraInfo);
}
19 changes: 9 additions & 10 deletions ncollide_geometry/query/point_internal/point_segment.rs
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Expand Up @@ -7,8 +7,7 @@ use math::{Point, Isometry};
impl<P: Point, M: Isometry<P>> PointQuery<P, M> for Segment<P> {
#[inline]
fn project_point(&self, m: &M, pt: &P, solid: bool) -> PointProjection<P> {
let (projection, _) = self.project_point_with_extra_info(m, pt, solid);
projection
self.project_point_with_extra_info(m, pt, solid).0
}

// NOTE: the default implementation of `.distance_to_point(...)` will return the error that was
Expand All @@ -29,29 +28,29 @@ impl<P: Point, M: Isometry<P>> RichPointQuery<P, M> for Segment<P> {
let sqnab = na::norm_squared(&ab);

let proj;
let position_on_segment;
let bcoords;

if ab_ap <= na::zero() {
// Voronoï region of vertex 'a'.
position_on_segment = na::zero();
proj = m.transform_point(self.a());
bcoords = na::zero();
proj = m.transform_point(self.a());
}
else if ab_ap >= sqnab {
// Voronoï region of vertex 'b'.
position_on_segment = na::one();
proj = m.transform_point(self.b());
bcoords = na::one();
proj = m.transform_point(self.b());
}
else {
assert!(sqnab != na::zero());

// Voronoï region of the segment interior.
position_on_segment = ab_ap / sqnab;
proj = m.transform_point(&(*self.a() + ab * position_on_segment));
bcoords = ab_ap / sqnab;
proj = m.transform_point(&(*self.a() + ab * bcoords));
}

// FIXME: is this acceptable?
let inside = relative_eq!(proj, *pt);

(PointProjection::new(inside, proj), position_on_segment)
(PointProjection::new(inside, proj), bcoords)
}
}
103 changes: 54 additions & 49 deletions ncollide_geometry/query/point_internal/point_triangle.rs
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
use na;
use na::{self, Vector3};
use shape::Triangle;
use query::{PointQuery, PointProjection, RichPointQuery};
use math::{Point, Isometry};
Expand Down Expand Up @@ -30,12 +30,11 @@ impl<P: Point, M: Isometry<P>> RichPointQuery<P, M> for Triangle<P> {
// Implementing this trait while providing no projection info might seem
// nonsensical, but it actually makes it possible to complete the
// `RichPointQuery` implementation for `BaseMesh`.
type ExtraInfo = ();
type ExtraInfo = Vector3<P::Real>;

#[inline]
fn project_point_with_extra_info(&self, m: &M, pt: &P, solid: bool)
-> (PointProjection<P>, Self::ExtraInfo)
{
-> (PointProjection<P>, Self::ExtraInfo) {
/*
* This comes from the book `Real Time Collision Detection`.
* This is actually a trivial Voronoï region based approach, except that great care has
Expand All @@ -57,7 +56,7 @@ impl<P: Point, M: Isometry<P>> RichPointQuery<P, M> for Triangle<P> {

if d1 <= na::zero() && d2 <= na::zero() {
// Voronoï region of `a`.
return (compute_result(pt, m.transform_point(&a)), ());
return (compute_result(pt, m.transform_point(&a)), Vector3::x());
}

let bp = p - b;
Expand All @@ -66,14 +65,15 @@ impl<P: Point, M: Isometry<P>> RichPointQuery<P, M> for Triangle<P> {

if d3 >= na::zero() && d4 <= d3 {
// Voronoï region of `b`.
return (compute_result(pt, m.transform_point(&b)), ());
return (compute_result(pt, m.transform_point(&b)), Vector3::y());
}

let vc = d1 * d4 - d3 * d2;
if vc <= na::zero() && d1 >= na::zero() && d3 <= na::zero() {
// Voronoï region of `ab`.
let v = d1 / (d1 - d3);
return (compute_result(pt, m.transform_point(&(a + ab * v))), ());
let bcoords = Vector3::new(na::one::<P::Real>() - v, v, na::zero());
return (compute_result(pt, m.transform_point(&(a + ab * v))), bcoords);
}

let cp = p - c;
Expand All @@ -82,76 +82,81 @@ impl<P: Point, M: Isometry<P>> RichPointQuery<P, M> for Triangle<P> {

if d6 >= na::zero() && d5 <= d6 {
// Voronoï region of `c`.
return (compute_result(pt, m.transform_point(&c)), ());
return (compute_result(pt, m.transform_point(&c)), Vector3::z());
}

let vb = d5 * d2 - d1 * d6;

if vb <= na::zero() && d2 >= na::zero() && d6 <= na::zero() {
// Voronoï region of `ac`.
let w = d2 / (d2 - d6);
return (compute_result(pt, m.transform_point(&(a + ac * w))), ());
let bcoords = Vector3::new(na::one::<P::Real>() - w, na::zero(), w);
return (compute_result(pt, m.transform_point(&(a + ac * w))), bcoords);
}

let va = d3 * d6 - d5 * d4;
if va <= na::zero() && d4 - d3 >= na::zero() && d5 - d6 >= na::zero() {
// Voronoï region of `bc`.
let w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
return (compute_result(pt, m.transform_point(&(b + (c - b) * w))), ());
let bcoords = Vector3::new(na::zero(), na::one::<P::Real>() - w, w);
return (compute_result(pt, m.transform_point(&(b + (c - b) * w))), bcoords);
}

// Voronoï region of the face.
if na::dimension::<P::Vector>() != 2 {
// If we work in 2d, we really are inside of the object.
if na::dimension::<P::Vector>() != 2 || solid {
let denom = na::one::<P::Real>() / (va + vb + vc);
let v = vb * denom;
let w = vc * denom;
let bcoords = Vector3::new(na::one::<P::Real>() - v - w, v, w);
let proj = m.transform_point(&(a + ab * v + ac * w));
let inside = na::dimension::<P::Vector>() == 2 || relative_eq!(proj, *pt);

return (compute_result(pt, m.transform_point(&(a + ab * v + ac * w))), ());
(PointProjection::new(inside, proj), bcoords)
}
else {
// Special treatement if we work in 2d because in this case we really are inside of the
// object.
if solid {
(PointProjection::new(true, *pt), ())
// Not-solid 2D projection.
// We have to project on the closest edge.

// FIXME: this might be optimizable.
let v = d1 / (d1 - d3); // proj on ab = a + ab * v
let w = d2 / (d2 - d6); // proj on ac = a + ac * w
let u = (d4 - d3) / ((d4 - d3) + (d5 - d6)); // proj on bc = b + bc * u

let bc = c - b;
let d_ab = na::norm_squared(&ap) - (na::norm_squared(&ab) * v * v);
let d_ac = na::norm_squared(&ap) - (na::norm_squared(&ac) * u * u);
let d_bc = na::norm_squared(&bp) - (na::norm_squared(&bc) * w * w);

let proj;
let bcoords;

if d_ab < d_ac {
if d_ab < d_bc {
// ab
proj = m.transform_point(&(a + ab * v));
bcoords = Vector3::new(na::one::<P::Real>() - v, v, na::zero());
}
else {
// bc
proj = m.transform_point(&(b + bc * u));
bcoords = Vector3::new(na::zero(), na::one::<P::Real>() - v, v);
}
}
else {
// We have to project on the closest edge.

// FIXME: this might be optimizable.
let v = d1 / (d1 - d3); // proj on ab = a + ab * v
let w = d2 / (d2 - d6); // proj on ac = a + ac * w
let u = (d4 - d3) / ((d4 - d3) + (d5 - d6)); // proj on bc = b + bc * u

let bc = c - b;
let d_ab = na::norm_squared(&ap) - (na::norm_squared(&ab) * v * v);
let d_ac = na::norm_squared(&ap) - (na::norm_squared(&ac) * u * u);
let d_bc = na::norm_squared(&bp) - (na::norm_squared(&bc) * w * w);

let proj;

if d_ab < d_ac {
if d_ab < d_bc {
// ab
proj = m.transform_point(&(a + ab * v));
}
else {
// bc
proj = m.transform_point(&(b + bc * u));
}
if d_ac < d_bc {
// ac
proj = m.transform_point(&(a + ac * w));
bcoords = Vector3::new(na::one::<P::Real>() - w, na::zero(), w);
}
else {
if d_ac < d_bc {
// ac
proj = m.transform_point(&(a + ac * w));
}
else {
// bc
proj = m.transform_point(&(b + bc * u));
}
// bc
proj = m.transform_point(&(b + bc * u));
bcoords = Vector3::new(na::zero(), na::one::<P::Real>() - u, u);
}

(PointProjection::new(true, proj), ())
}

(PointProjection::new(true, proj), bcoords)
}
}
}