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//! Common and trivial geometric primitives.
// NOTE: in this module, the type parameters <P,E> usually stand for Position and Extent.
use num_traits::{real::Real, FloatConst, Zero, One, AsPrimitive};
use approx::RelativeEq;
use std::ops::*;
use std::ops::Add;
use crate::ops::Clamp;
// WISH: add useful impls to this module (inclusing basic conversions from rect to vec pairs)
// WISH: lerp for all shapes
// WISH: More intersections (e.g line_segment vs box, etc)
macro_rules! geom_impl_line_segment {
($LineSegment:ident $Vec:ident) => {
impl<T> From<Range<$Vec<T>>> for $LineSegment<T> {
fn from(range: Range<$Vec<T>>) -> Self {
let Range { start, end } = range;
Self { start, end }
}
}
impl<T> $LineSegment<T> {
/// Converts this line segment into a range of points.
pub fn into_range(self) -> Range<$Vec<T>> {
let Self { start, end } = self;
Range { start, end }
}
/// Project the given point onto the line segment (equivalent to 'snapping' the point
/// to the closest point on the line segment).
pub fn projected_point(self, p: $Vec<T>) -> $Vec<T> where T: Real + Add<T, Output=T> + RelativeEq {
let len_sq = self.start.distance_squared(self.end);
if len_sq.relative_eq(&Zero::zero(), T::default_epsilon(), T::default_max_relative()) {
self.start
} else {
let t = ((p - self.start).dot(self.end - self.start) / len_sq)
.max(Zero::zero())
.min(One::one());
self.start + (self.end - self.start) * t
}
}
/// Get the smallest distance between the line segment and a point.
pub fn distance_to_point(self, p: $Vec<T>) -> T where T: Real + Add<T, Output=T> + RelativeEq {
self.projected_point(p).distance(p)
}
/// Converts this line to a line of another type, using the `as` conversion.
pub fn as_<D>(self) -> $LineSegment<D> where T: AsPrimitive<D>, D: 'static + Copy {
let Self { start, end } = self;
$LineSegment { start: start.as_(), end: end.as_() }
}
}
};
}
macro_rules! geom_impl_rect_or_rect3 {
(
$Rect:ident $Vec:ident $Extent:ident ($(($p_s:expr) $p:ident $split_at_p:ident)+) ($($e:ident)+)
$Aab:ident $into_aab:ident
contains_rect: $contains_rect:ident
contains_aab: $contains_aab:ident
collides_with_rect: $collides_with_rect:ident
collides_with_aab: $collides_with_aab:ident
collision_vector_with_rect: $collision_vector_with_rect:ident
collision_vector_with_aab: $collision_vector_with_aab:ident
) => {
impl<P,E> $Rect<P,E> {
/// Creates a new rectangle from position elements and extent elements.
pub fn new($($p: P,)+ $($e: E),+) -> Self {
Self { $($p,)+ $($e),+ }
}
/// Gets this rectangle's position.
pub fn position(self) -> $Vec<P> {
let Self { $($p,)+ .. } = self;
$Vec { $($p,)+ }
}
/// Sets this rectangle's position.
pub fn set_position(&mut self, p: $Vec<P>) {
$(self.$p = p.$p;)*
}
/// Gets this rectangle's extent (size).
pub fn extent(self) -> $Extent<E> {
let Self { $($e,)+ .. } = self;
$Extent { $($e,)+ }
}
/// Sets this rectangle's extent (size).
pub fn set_extent(&mut self, e: $Extent<E>) {
$(self.$e = e.$e;)*
}
/// Gets this rectangle's position and extent (size).
pub fn position_extent(self) -> ($Vec<P>, $Extent<E>) {
let Self { $($p,)+ $($e,)+ } = self;
($Vec { $($p,)+ }, $Extent { $($e,)+ })
}
/// Returns this rectangle, converted with the given closures (one for position
/// elements, the other for extent elements).
pub fn map<DP,DE,PF,EF>(self, pf: PF, ef: EF) -> $Rect<DP,DE>
where PF: FnMut(P) -> DP, EF: FnMut(E) -> DE
{
let Self { $($p,)+ $($e,)+ } = self;
let $Vec { $($p,)+ } = $Vec { $($p,)+ }.map(pf);
let $Extent { $($e,)+ } = $Extent { $($e,)+ }.map(ef);
$Rect { $($p,)+ $($e,)+ }
}
/// Converts this rectangle to a rectangle of another type, using the `as` conversion.
pub fn as_<DP,DE>(self) -> $Rect<DP,DE>
where P: AsPrimitive<DP>, DP: 'static + Copy,
E: AsPrimitive<DE>, DE: 'static + Copy
{
let Self { $($p,)+ $($e,)+ } = self;
let $Vec { $($p,)+ } = $Vec { $($p,)+ }.as_();
let $Extent { $($e,)+ } = $Extent { $($e,)+ }.as_();
$Rect { $($p,)+ $($e,)+ }
}
}
impl<T> $Rect<T,T> where T: Copy + Add<T, Output=T> {
/// Converts this into the matching axis-aligned bounding shape representation.
pub fn $into_aab(self) -> $Aab<T> {
self.into()
}
/// Does this rectangle contain the given point ?
pub fn contains_point(self, p: $Vec<T>) -> bool where T: PartialOrd {
self.$into_aab().contains_point(p)
}
/// Does this rectangle fully contain the given one ?
pub fn $contains_rect(self, other: Self) -> bool where T: PartialOrd {
self.$into_aab().$contains_aab(other.into())
}
/// Does this rectangle collide with another ?
pub fn $collides_with_rect(self, other: Self) -> bool where T: PartialOrd {
self.$into_aab().$collides_with_aab(other.into())
}
/// Gets this rectangle's center.
pub fn center(self) -> $Vec<T> where T: One + Div<T,Output=T> {
self.$into_aab().center()
}
}
impl<T> $Rect<T,T> where T: Copy + PartialOrd + Sub<T, Output=T> + Add<T, Output=T> {
/// Returns this shape so that it contains the given point.
pub fn expanded_to_contain_point(self, p: $Vec<T>) -> Self where T: PartialOrd {
self.$into_aab().expanded_to_contain_point(p).into()
}
/// Expands this shape so that it contains the given point.
pub fn expand_to_contain_point(&mut self, p: $Vec<T>) where T: PartialOrd {
*self = self.expanded_to_contain_point(p);
}
/// Gets the smallest rectangle that contains both this one and another.
pub fn union(self, other: Self) -> Self {
self.$into_aab().union(other.into()).into()
}
/// Gets the largest rectangle contained by both this one and another.
pub fn intersection(self, other: Self) -> Self {
self.$into_aab().intersection(other.into()).into()
}
/// Sets this rectangle to the union of itself with another.
pub fn expand_to_contain(&mut self, other: Self) {
*self = self.union(other);
}
/// Sets this rectangle to the intersection of itself with another.
pub fn intersect(&mut self, other: Self) {
*self = self.intersection(other);
}
/// Gets a vector that tells how much `self` penetrates `other`.
pub fn $collision_vector_with_rect(self, other: Self) -> $Vec<T>
where T: One + Div<T,Output=T>
{
self.$into_aab().$collision_vector_with_aab(other.into())
}
$(
/// Splits this shape in two, by a straight plane along the
#[doc=$p_s]
/// axis.
/// The returned tuple is `(low, high)`.
///
/// # Panics
/// `sp` is assumed to be a position along the
#[doc=$p_s]
/// axis that is within this shape's bounds.
pub fn $split_at_p(self, sp: T) -> [Self; 2] {
let s = self.$into_aab().$split_at_p(sp);
[s[0].into(), s[1].into()]
}
)+
}
impl<P,E> From<($Vec<P>, $Extent<E>)> for $Rect<P,E> {
fn from(t: ($Vec<P>, $Extent<E>)) -> Self {
let ($Vec { $($p,)+ }, $Extent { $($e,)+ }) = t;
Self { $($p,)+ $($e,)+ }
}
}
impl<T> From<$Aab<T>> for $Rect<T,T>
where T: Copy + Sub<T, Output=T>
{
fn from(aab: $Aab<T>) -> Self {
let $Extent { $($e,)+ } = (aab.max - aab.min).into();
Self {
$($p: aab.min.$p,)+
$($e,)+
}
}
}
impl<T> From<$Rect<T,T>> for $Aab<T>
where T: Copy + Add<T, Output=T>
{
fn from(rect: $Rect<T,T>) -> Self {
Self {
min: rect.position(),
max: rect.position() + rect.extent(),
}
}
}
};
}
macro_rules! geom_impl_aabr_or_aabb {
(
$Aab:ident $Vec:ident $Extent:ident ($(($p_s:expr) $p:ident $split_at_p:ident)+)
$Rect:ident $into_rect:ident
contains_aab: $contains_aab:ident
collides_with_aab: $collides_with_aab:ident
collision_vector_with_aab: $collision_vector_with_aab:ident
) => {
impl<T> $Aab<T> {
/// Is this bounding shape valid ?
/// True only if all elements of `self.min` are less than or equal to those of `self.max`.
pub fn is_valid(&self) -> bool where T: PartialOrd {
self.min.partial_cmple(&self.max).reduce_and()
}
/// Makes this bounding shape valid by swapping elements of `self.min` with `self.max` as needed.
pub fn make_valid(&mut self) where T: PartialOrd {
$(if self.min.$p > self.max.$p { std::mem::swap(&mut self.min.$p, &mut self.max.$p); })+
}
/// Returns this bounding shape made valid by swapping elements of `self.min` with `self.max` as needed.
pub fn made_valid(mut self) -> Self where T: PartialOrd {
self.make_valid();
self
}
/// Creates a new bounding shape from a single point.
pub fn new_empty(p: $Vec<T>) -> Self where T: Copy {
let (min, max) = (p, p);
Self { min, max }
}
/// Converts this bounding shape to the matching rectangle representation.
pub fn $into_rect(self) -> $Rect<T,T>
where T: Copy + Sub<T, Output=T>
{
self.into()
}
/// Gets this bounding shape's center.
pub fn center(self) -> $Vec<T>
where T: Copy + One + Add<T,Output=T> + Div<T,Output=T>
{
(self.min + self.max) / (T::one() + T::one())
}
/// Gets this bounding shape's total size.
pub fn size(self) -> $Extent<T>
where T: Copy + Sub<T, Output=T>
{
self.$into_rect().extent()
}
/// Gets this bounding shape's half size.
pub fn half_size(self) -> $Extent<T>
where T: Copy + Sub<T, Output=T> + One + Div<T,Output=T> + Add<T, Output=T>
{
self.size() / (T::one() + T::one())
}
/// Gets the smallest bounding shape that contains both this one and another.
pub fn union(self, other: Self) -> Self where T: PartialOrd {
Self {
min: $Vec::partial_min(self.min, other.min),
max: $Vec::partial_max(self.max, other.max),
}
}
/// Gets the largest bounding shape contained by both this one and another.
pub fn intersection(self, other: Self) -> Self where T: PartialOrd {
Self {
min: $Vec::partial_max(self.min, other.min),
max: $Vec::partial_min(self.max, other.max),
}
}
/// Sets this bounding shape to the union of itself with another.
pub fn expand_to_contain(&mut self, other: Self) where T: Copy + PartialOrd {
*self = self.union(other);
}
/// Sets this bounding shape to the intersection of itself with another.
pub fn intersect(&mut self, other: Self) where T: Copy + PartialOrd {
*self = self.intersection(other);
}
/// Gets a copy of this shape so that it contains the given point.
pub fn expanded_to_contain_point(self, p: $Vec<T>) -> Self where T: Copy + PartialOrd {
self.union(Self::new_empty(p))
}
/// Expands this shape so that it contains the given point.
pub fn expand_to_contain_point(&mut self, p: $Vec<T>) where T: Copy + PartialOrd {
*self = self.expanded_to_contain_point(p);
}
/// Does this bounding shape contain the given point ?
pub fn contains_point(self, p: $Vec<T>) -> bool
where T: PartialOrd
{
true $(&& self.min.$p <= p.$p && p.$p <= self.max.$p)+
}
/// Does this bounding shape fully contain another ?
pub fn $contains_aab(self, other: Self) -> bool
where T: PartialOrd
{
true $(&& self.min.$p <= other.min.$p && other.max.$p <= self.max.$p)+
}
/// Does this bounding shape collide with another ?
pub fn $collides_with_aab(self, other: Self) -> bool
where T: PartialOrd
{
true $(&& self.max.$p > other.min.$p && self.min.$p < other.max.$p)+
}
/// Gets a vector that tells how much `self` penetrates `other`.
pub fn $collision_vector_with_aab(self, other: Self) -> $Vec<T>
where T: Copy + PartialOrd + Sub<T, Output=T> + One + Add<T,Output=T> + Div<T,Output=T>
{
let (b1, b2) = (self, other);
let (c1, c2) = (b1.center(), b2.center());
$Vec { $($p: if c1.$p < c2.$p {
b1.max.$p - b2.min.$p
} else {
b1.min.$p - b2.max.$p
}),+}
}
/// Project the given point into the bounding shape (equivalent to 'snapping' the point
/// to the closest point in the bounding shape).
pub fn projected_point(self, p: $Vec<T>) -> $Vec<T>
where T: Clamp
{
p.clamped(self.min, self.max)
}
/// Get the smallest distance between the bounding shape and a point.
pub fn distance_to_point(self, p: $Vec<T>) -> T where T: Clamp + Real + Add<T, Output=T> + RelativeEq {
self.projected_point(p).distance(p)
}
$(
/// Splits this shape in two, by a straight plane along the
#[doc=$p_s]
/// axis.
/// The returned tuple is `(low, high)`.
///
/// # Panics
/// `sp` is assumed to be a position along the
#[doc=$p_s]
/// axis that is within this shape's bounds.
pub fn $split_at_p(self, sp: T) -> [Self; 2] where T: Copy + PartialOrd {
debug_assert!(sp >= self.min.$p);
debug_assert!(sp <= self.max.$p);
let low = Self {
min: self.min,
max: { let mut v = self.max; v.$p = sp; v },
};
let high = Self {
min: { let mut v = self.min; v.$p = sp; v },
max: self.max,
};
[low, high]
}
)+
/// Returns this bounding shape, converted element-wise using the given closure.
pub fn map<D,F>(self, mut f: F) -> $Aab<D> where F: FnMut(T) -> D
{
let Self { min, max } = self;
let $Vec { $($p,)+ } = min;
let min = $Vec { $($p: f($p),)+ };
let $Vec { $($p,)+ } = max;
let max = $Vec { $($p: f($p),)+ };
$Aab { min, max }
}
/// Converts this rectangle to a rectangle of another type, using the `as` conversion.
pub fn as_<D>(self) -> $Aab<D> where T: AsPrimitive<D>, D: 'static + Copy {
let Self { min, max } = self;
$Aab { min: min.as_(), max: max.as_() }
}
}
};
}
macro_rules! geom_impl_disk_or_sphere {
(
$Shape:ident ($Shape_s:expr) $Vec:ident ($($p:ident)+)
$Extent:ident
$Rect:ident $rect:ident
$Aab:ident $aab:ident
collides_with_other: $collides_with_other:ident
collision_vector_with_other: $collision_vector_with_other:ident
) => {
impl<P,E> $Shape<P,E> {
/// Creates a new
#[doc=$Shape_s]
/// from `center` and `radius`.
pub fn new(center: $Vec<P>, radius: E) -> Self {
Self { center, radius }
}
/// Creates a new
#[doc=$Shape_s]
/// from `center` and a `radius` equal to one.
pub fn unit(center: $Vec<P>) -> Self where E: One {
Self { center, radius: One::one() }
}
/// Creates a new
#[doc=$Shape_s]
/// from `center` and a `radius` equal to zero.
pub fn point(center: $Vec<P>) -> Self where E: Zero {
Self { center, radius: Zero::zero() }
}
/// Gets the value of twice the radius.
pub fn diameter(self) -> E where E: Copy + Add<Output=E> {
self.radius + self.radius
}
/// Gets the bounding rectangle for this shape.
pub fn $rect(self) -> $Rect<P,E>
where P: Sub<P,Output=P> + From<E> + Copy, E: Copy + Add<E,Output=E>
{
$Rect::from((
self.center - P::from(self.radius),
$Extent::broadcast(self.diameter())
))
}
}
impl<T> $Shape<T,T> where T: Copy + Add<T,Output=T> + Sub<T,Output=T> {
/// Gets this shape's bounds.
pub fn $aab(self) -> $Aab<T> {
$Aab {
min: self.center - self.radius,
max: self.center + self.radius,
}
}
}
impl<T: Real + Add<T, Output=T>> $Shape<T,T> {
/// Does this shape contain the given point ?
pub fn contains_point(self, p: $Vec<T>) -> bool where T: PartialOrd {
self.center.distance(p) <= self.radius
}
/// Does this shape collide with another ?
pub fn $collides_with_other(self, other: Self) -> bool where T: PartialOrd {
self.center.distance(other.center) <= (self.radius + other.radius)
}
// XXX: This remains to be tested!
/// Gets a vector that tells how much this shape penetrates another.
pub fn $collision_vector_with_other(self, other: Self) -> $Vec<T> {
let v = other.center - self.center;
let mag = self.radius + other.radius - v.magnitude();
v.normalized() * mag
}
}
};
}
// NOTE: There's never a sane Default for this, so don't implement or derive it!!
/// Data that represents distance offsets of frustum planes from an origin.
#[derive(Debug, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct FrustumPlanes<T> {
pub left: T,
pub right: T,
pub bottom: T,
pub top: T,
pub near: T,
pub far: T,
}
macro_rules! geom_complete_mod {
($mod:ident) => {
use crate::vec::$mod::*;
// XXX: Beware when using code that assumes that Y points downards.
// Luckily, our matrix functions (those that receive a viewport) do not!
/// 2D rectangle, represented by a bottom-left position, and 2D extents.
///
/// Most operations on a `Rect` are better done by converting it to
/// `Aabr` form. In fact, most existing code in the wild implicitly does this
/// and so does this crate.
///
/// `Aabr` structs are often more convenient, faster and probably less confusing.
/// The `Rect` type is provided because it exists for a lot of APIs (including
/// some system APIs, OpenGL, and others).
///
/// Please note that in most APIs in the wild (but **NOT** in `vek`), the Y axis
/// is treated as pointing **downwards** because it's the one of window space.
///
/// Keeping the Y axis upwards is a lot more convenient implementation-wise,
/// and still matches the convention used in 3D spaces.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
pub struct Rect<P, E> {
/// X position of the **bottom-left** corner.
pub x: P,
/// Y position of the **bottom-left** corner.
pub y: P,
/// Width.
pub w: E,
/// Height, **with Y axis going upwards**.
pub h: E,
}
geom_impl_rect_or_rect3!{
Rect Vec2 Extent2 (("x") x split_at_x ("y") y split_at_y) (w h)
Aabr into_aabr
contains_rect: contains_rect
contains_aab: contains_aabr
collides_with_rect: collides_with_rect
collides_with_aab: collides_with_aabr
collision_vector_with_rect: collision_vector_with_rect
collision_vector_with_aab: collision_vector_with_aabr
}
/// Axis-aligned Bounding Rectangle (2D), represented by `min` and `max` points.
///
/// **N.B:** You are responsible for ensuring that all respective elements of
/// `min` are indeed less than or equal to those of `max`.
/// The `is_valid()`, `make_valid()` and `made_valid()` methods are designed to help you
/// with this.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
pub struct Aabr<T> {
/// Minimum coordinates of bounds.
pub min: Vec2<T>,
/// Maximum coordinates of bounds.
pub max: Vec2<T>,
}
impl<T> From<Aabb<T>> for Aabr<T> {
fn from(aabb: Aabb<T>) -> Self {
Self {
min: aabb.min.into(),
max: aabb.max.into(),
}
}
}
geom_impl_aabr_or_aabb!{
Aabr Vec2 Extent2 (("x") x split_at_x ("y") y split_at_y)
Rect into_rect
contains_aab: contains_aabr
collides_with_aab: collides_with_aabr
collision_vector_with_aab: collision_vector_with_aabr
}
/// A `Rect` extended to 3D.
///
/// This would have been named `Box`, but it was "taken" by the standard library already.
///
/// You should probably use `Aabb` because it is less confusing.
/// See also `Rect` for a short discussion on the topic.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
pub struct Rect3<P,E> {
/// X position of the **bottom-left-near** corner.
pub x: P,
/// Y position of the **bottom-left-near** corner.
pub y: P,
/// Z position of the **bottom-left-near** corner.
pub z: P,
/// Width.
pub w: E,
/// Height, **with Y axis going upwards**.
pub h: E,
/// Depth, **with Z axis going forwards**.
pub d: E,
}
geom_impl_rect_or_rect3!{
Rect3 Vec3 Extent3 (("x") x split_at_x ("y") y split_at_y ("z") z split_at_z) (w h d)
Aabb into_aabb
contains_rect: contains_rect3
contains_aab: contains_aabb
collides_with_rect: collides_with_rect3
collides_with_aab: collides_with_aabb
collision_vector_with_rect: collision_vector_with_rect3
collision_vector_with_aab: collision_vector_with_aabb
}
/// Axis-aligned Bounding Box (3D), represented by `min` and `max` points.
///
/// **N.B:** You are responsible for ensuring that all respective elements of
/// `min` are indeed less than or equal to those of `max`.
/// The `is_valid()`, `make_valid()` and `made_valid()` methods are designed to help you
/// with this.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
pub struct Aabb<T> {
/// Minimum coordinates of bounds.
pub min: Vec3<T>,
/// Maximum coordinates of bounds.
pub max: Vec3<T>,
}
geom_impl_aabr_or_aabb!{
Aabb Vec3 Extent3 (("x") x split_at_x ("y") y split_at_y ("z") z split_at_z)
Rect3 into_rect3
contains_aab: contains_aabb
collides_with_aab: collides_with_aabb
collision_vector_with_aab: collision_vector_with_aabb
}
// NOTE: Only implement axis-aligned primitives (a.k.a don't go on a rampage).
//
// Don't write, e.g a "Disk in 3D-space" structure, because users would rather
// represent it with a (Disk, z, orientation) tuple or anything else that suits their particular needs.
//
// On the other hand, everybody agrees that a minimal "Disk" struct is a position+radius pair.
// (even if it's just expressed as a radius with no
// position, then fine, just use the radius as-is, without making it it a new struct).
//
// Any other info, such as fill color, border thickness, etc. are just extras that users can
// put on top (see composition over inheritance, etc).
/// Disk (2D), represented by center and radius.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct Disk<P,E> {
pub center: Vec2<P>,
pub radius: E,
}
impl<P,E> Disk<P,E> {
/// Gets this disk's circumference.
pub fn circumference(self) -> E
where E: Copy + FloatConst + Mul<Output=E> + Add<Output=E>
{
let pi = E::PI();
(pi + pi) * self.radius
}
/// Gets this disk's area.
pub fn area(self) -> E where E: Copy + FloatConst + Mul<Output=E> {
let r = self.radius;
E::PI()*r*r
}
}
geom_impl_disk_or_sphere!{
Disk ("Disk") Vec2 (x y)
Extent2 Rect rect Aabr aabr
collides_with_other: collides_with_disk
collision_vector_with_other: collision_vector_with_disk
}
/// Sphere (3D), represented by center and radius.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct Sphere<P,E> {
pub center: Vec3<P>,
pub radius: E,
}
impl<P,E> Sphere<P,E> {
/// Gets this sphere's surface area.
pub fn surface_area(self) -> E where E: Copy + One + FloatConst + Add<Output=E> + Mul<Output=E> {
let four = E::one() + E::one() + E::one() + E::one();
let r = self.radius;
four*E::PI()*r*r
}
/// Gets this sphere's volume.
pub fn volume(self) -> E where E: Copy + One + FloatConst + Add<Output=E> + Mul<Output=E> + Div<Output=E> {
let four = E::one() + E::one() + E::one() + E::one();
let three = E::one() + E::one() + E::one();
let r = self.radius;
(four*E::PI()*r*r*r)/three
}
}
geom_impl_disk_or_sphere!{
Sphere ("Sphere") Vec3 (x y z)
Extent3 Rect3 rect3 Aabb aabb
collides_with_other: collides_with_sphere
collision_vector_with_other: collision_vector_with_sphere
}
/// Ellipsis (2D), represented by center and radius in both axii.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct Ellipsis<P,E> {
pub center: Vec2<P>,
pub radius: Extent2<E>,
}
/// Nobody can possibly use this ???
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct Potato<P,E> {
pub center: Vec3<P>,
pub radius: Extent3<E>,
}
/// 2D Line segment, represented by two points, `start` and `end`.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct LineSegment2<T> {
pub start: Vec2<T>,
pub end: Vec2<T>,
}
/// 3D Line segment, represented by two points, `start` and `end`.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
#[allow(missing_docs)]
pub struct LineSegment3<T> {
pub start: Vec3<T>,
pub end: Vec3<T>,
}
geom_impl_line_segment!{LineSegment2 Vec2}
geom_impl_line_segment!{LineSegment3 Vec3}
/// 3D ray, represented by a starting point and a normalized direction vector.
#[derive(Debug, Default, Clone, Copy, Hash, Eq, PartialEq, /*Ord, PartialOrd*/)]
#[cfg_attr(feature="serde", derive(Serialize, Deserialize))]
pub struct Ray<T> {
/// The ray's starting point.
pub origin: Vec3<T>,
/// The ray's direction. **Methods expect it to be normalized**.
pub direction: Vec3<T>,
}
impl<T: Real + Add<T, Output=T>> Ray<T> {
/// Creates a `Ray` from a starting point and direction.
///
/// This doesn't check if `direction` is normalized, because either you know it is, or
/// it isn't and maybe it doesn't matter for your use case.
pub fn new(origin: Vec3<T>, direction: Vec3<T>) -> Self {
Self { origin, direction }
}
/// Tests if this ray intersects the given triangle, returning the distance from
/// the ray's origin along its direction where the intersection lies.
///
/// If the returned value is `Some(x)` where `x < EPSILON`, then you should
/// assume there was a line intersection, **NOT** a ray intersection.
///
/// This uses the [Möller–Trumbore intersection algorithm](https://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm).
pub fn triangle_intersection(&self, tri: [Vec3<T>; 3]) -> Option<T> {
let (v0, v1, v2) = (tri[0], tri[1], tri[2]);
let edge1 = v1 - v0;
let edge2 = v2 - v0;
let h = self.direction.cross(edge2);
let a = edge1.dot(h);
if a > -T::epsilon() && a < T::epsilon() {
return None;
}
let f = a.recip();
let s = self.origin - v0;
let u = f * s.dot(h);
if u < T::zero() || u > T::one() {
return None;
}
let q = s.cross(edge1);
let v = f * self.direction.dot(q);
if v < T::zero() || u + v > T::one() {
return None;
}
Some(f * edge2.dot(q))
}
}
}
}
#[cfg(all(nightly, feature="repr_simd"))]
pub mod repr_simd {
//! Basic geometric primitives that use `#[repr(simd)]` vectors.
use super::*;
geom_complete_mod!(repr_simd);
}
pub mod repr_c {
//! Basic geometric primitives that use `#[repr(C)]` vectors.
use super::*;
geom_complete_mod!(repr_c);
}
pub use self::repr_c::*;
#[cfg(test)]
mod tests {
use super::*;
use crate::vec::{Vec2, Vec3};
#[test] fn rect_center() {
let min = Vec2::new(-1_f32, -1.);
let max = -min;
let aabr = Aabr { min, max };
assert_relative_eq!(aabr.center(), Vec2::zero());
let rect = aabr.into_rect();
assert_relative_eq!(rect.center(), Vec2::zero());
}
#[test] fn rect3_center() {
let min = Vec3::new(-1_f32, -1., -1.);
let max = -min;
let aabb = Aabb { min, max };
assert_relative_eq!(aabb.center(), Vec3::zero());
let rect3 = aabb.into_rect3();
assert_relative_eq!(rect3.center(), Vec3::zero());
}
#[test] fn projected_point() {
let segment = LineSegment2 { start: Vec2::new(-5_f32, 5.), end: Vec2::new(5., -5.0) };
assert_relative_eq!(segment.start, segment.projected_point(Vec2::new(-4., 7.)));
assert_relative_eq!(segment.end, segment.projected_point(Vec2::new(7., -4.)));
assert_relative_eq!(Vec2::zero(), segment.projected_point(Vec2::new(1., 1.)));
let segment = LineSegment3 { start: Vec3::new(-5_f32, -0., 5.), end: Vec3::new(5., 0., -5.0) };
assert_relative_eq!(Vec3::zero(), segment.projected_point(Vec3::new(-0., -1., -0.)));
}
#[test] fn distance_to_point() {
let segment = LineSegment2 { start: Vec2::new(-5_f32, 5.), end: Vec2::new(5., -5.0) };
assert_relative_eq!(2.0f32.sqrt(), segment.distance_to_point(Vec2::new(-1., -1.)));
let segment = LineSegment3 { start: Vec3::new(-5_f32, 0., 5.), end: Vec3::new(5., 0., -5.) };
assert_relative_eq!(2.0f32.sqrt(), segment.distance_to_point(Vec3::new(-1., 0., -1.)));
}
}