Files
strafe-project/engine/physics/src/minimum_difference.rs

761 lines
20 KiB
Rust

use strafesnet_common::integer::vec3;
use strafesnet_common::integer::vec3::Vector3;
use strafesnet_common::integer::{Fixed,Planar64Vec3};
use crate::model::{DirectedEdge,FEV,MeshQuery,MinkowskiMesh,MinkowskiVert};
// This algorithm is based on Lua code
// written by Trey Reynolds in 2021
type Simplex<const N:usize>=[MinkowskiVert;N];
#[derive(Clone,Copy)]
enum Simplex1_3{
Simplex1(Simplex<1>),
Simplex2(Simplex<2>),
Simplex3(Simplex<3>),
}
impl Simplex1_3{
fn push_front(self,v:MinkowskiVert)->Simplex2_4{
match self{
Simplex1_3::Simplex1([v0])=>Simplex2_4::Simplex2([v,v0]),
Simplex1_3::Simplex2([v0,v1])=>Simplex2_4::Simplex3([v,v0,v1]),
Simplex1_3::Simplex3([v0,v1,v2])=>Simplex2_4::Simplex4([v,v0,v1,v2]),
}
}
}
enum Simplex2_4{
Simplex2(Simplex<2>),
Simplex3(Simplex<3>),
Simplex4(Simplex<4>),
}
/*
local function absDet(r, u, v, w)
if w then
return math.abs((u - r):Cross(v - r):Dot(w - r))
elseif v then
return (u - r):Cross(v - r).magnitude
elseif u then
return (u - r).magnitude
else
return 1
end
end
*/
impl Simplex2_4{
fn det_is_zero(&self,mesh:&MinkowskiMesh)->bool{
match self{
&Self::Simplex4([p0,p1,p2,p3])=>{
let p0=mesh.vert(p0);
let p1=mesh.vert(p1);
let p2=mesh.vert(p2);
let p3=mesh.vert(p3);
(p1-p0).cross(p2-p0).dot(p3-p0)==Fixed::ZERO
},
&Self::Simplex3([p0,p1,p2])=>{
let p0=mesh.vert(p0);
let p1=mesh.vert(p1);
let p2=mesh.vert(p2);
(p1-p0).cross(p2-p0)==vec3::zero()
},
&Self::Simplex2([p0,p1])=>{
let p0=mesh.vert(p0);
let p1=mesh.vert(p1);
p1-p0==vec3::zero()
}
}
}
}
/*
local function choosePerpendicularDirection(d)
local x, y, z = d.x, d.y, d.z
local best = math.min(x*x, y*y, z*z)
if x*x == best then
return Vector3.new(y*y + z*z, -x*y, -x*z)
elseif y*y == best then
return Vector3.new(-x*y, x*x + z*z, -y*z)
else
return Vector3.new(-x*z, -y*z, x*x + y*y)
end
end
*/
fn choose_perpendicular_direction(d:Planar64Vec3)->Planar64Vec3{
let x=d.x.abs();
let y=d.y.abs();
let z=d.z.abs();
if x<y&&x<z{
Vector3::new([Fixed::ZERO,-d.z,d.y])
}else if y<z{
Vector3::new([d.z,Fixed::ZERO,-d.x])
}else{
Vector3::new([-d.y,d.x,Fixed::ZERO])
}
}
const fn choose_any_direction()->Planar64Vec3{
vec3::X
}
fn reduce1(
[v0]:Simplex<1>,
mesh:&MinkowskiMesh,
point:Planar64Vec3,
)->Reduced{
// --debug.profilebegin("reduceSimplex0")
// local a = a1 - a0
let p0=mesh.vert(v0);
// local p = -a
let p=-(p0+point);
// local direction = p
let mut dir=p;
// if direction.magnitude == 0 then
// direction = chooseAnyDirection()
if dir==vec3::zero(){
dir=choose_any_direction();
}
// return direction, a0, a1
Reduced{
dir,
simplex:Simplex1_3::Simplex1([v0]),
}
}
// local function reduceSimplex1(a0, a1, b0, b1)
fn reduce2(
[v0,v1]:Simplex<2>,
mesh:&MinkowskiMesh,
point:Planar64Vec3,
)->Reduced{
// --debug.profilebegin("reduceSimplex1")
// local a = a1 - a0
// local b = b1 - b0
let p0=mesh.vert(v0);
let p1=mesh.vert(v1);
// local p = -a
// local u = b - a
let p=-(p0+point);
let u=p1-p0;
// -- modify to take into account the radiuses
// local p_u = p:Dot(u)
let p_u=p.dot(u);
// if p_u >= 0 then
if !p_u.is_negative(){
// local direction = u:Cross(p):Cross(u)
let direction=u.cross(p).cross(u);
// if direction.magnitude == 0 then
if direction==vec3::zero(){
return Reduced{
dir:choose_perpendicular_direction(u),
simplex:Simplex1_3::Simplex2([v0,v1]),
};
}
// -- modify the direction to take into account a0R and b0R
// return direction, a0, a1, b0, b1
return Reduced{
dir:direction.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
};
}
// local direction = p
let mut dir=p;
// if direction.magnitude == 0 then
if dir==vec3::zero(){
dir=choose_perpendicular_direction(u);
}
// return direction, a0, a1
Reduced{
dir,
simplex:Simplex1_3::Simplex1([v0]),
}
}
// local function reduceSimplex2(a0, a1, b0, b1, c0, c1)
fn reduce3(
[v0,mut v1,v2]:Simplex<3>,
mesh:&MinkowskiMesh,
point:Planar64Vec3,
)->Reduced{
// --debug.profilebegin("reduceSimplex2")
// local a = a1 - a0
// local b = b1 - b0
// local c = c1 - c0
let p0=mesh.vert(v0);
let p1=mesh.vert(v1);
let p2=mesh.vert(v2);
// local p = -a
// local u = b - a
// local v = c - a
let p=-(p0+point);
let mut u=p1-p0;
let v=p2-p0;
// local uv = u:Cross(v)
// local up = u:Cross(p)
// local pv = p:Cross(v)
// local uv_up = uv:Dot(up)
// local uv_pv = uv:Dot(pv)
let mut uv=u.cross(v);
let mut up=u.cross(p);
let pv=p.cross(v);
let uv_up=uv.dot(up);
let uv_pv=uv.dot(pv);
// if uv_up >= 0 and uv_pv >= 0 then
if !uv_up.is_negative()&&!uv_pv.is_negative(){
// local uvp = uv:Dot(p)
let uvp=uv.dot(p);
// local direction = uvp < 0 and -uv or uv
let direction=if uvp.is_negative(){
-uv
}else{
uv
};
// return direction, a0, a1, b0, b1, c0, c1
return Reduced{
dir:direction.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex3([v0,v1,v2]),
};
}
// local u_u = u:Dot(u)
// local v_v = v:Dot(v)
// local uDist = uv_up/(u_u*v.magnitude)
// local vDist = uv_pv/(v_v*u.magnitude)
// local minDist2 = math.min(uDist, vDist)
let u_dist=uv_up*v.length();
let v_dist=uv_pv*u.length();
// if vDist == minDist2 then
if v_dist<u_dist{
u=v;
up=-pv;
uv=-uv;
// b0 = c0
// b1 = c1
v1=v2;
}
// local p_u = p:Dot(u)
let p_u=p.dot(u);
// if p_u >= 0 then
if !p_u.is_negative(){
// local direction = up:Cross(u)
let direction=up.cross(u);
// if direction.magnitude == 0 then
if direction==vec3::zero(){
// direction = uv
return Reduced{
dir:uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
};
}
// return direction, a0, a1, b0, b1
return Reduced{
dir:direction.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
};
}
// local direction = p
let dir=p;
// if direction.magnitude == 0 then
if dir==vec3::zero(){
// direction = uv
return Reduced{
dir:uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex1([v0]),
};
}
// return direction, a0, a0
Reduced{
dir,
simplex:Simplex1_3::Simplex1([v0]),
}
}
// local function reduceSimplex3(a0, a1, b0, b1, c0, c1, d0, d1)
fn reduce4(
[v0,mut v1,mut v2,v3]:Simplex<4>,
mesh:&MinkowskiMesh,
point:Planar64Vec3,
)->Reduce{
// --debug.profilebegin("reduceSimplex3")
// local a = a1 - a0
// local b = b1 - b0
// local c = c1 - c0
// local d = d1 - d0
let p0=mesh.vert(v0);
let p1=mesh.vert(v1);
let p2=mesh.vert(v2);
let p3=mesh.vert(v3);
// local p = -a
// local u = b - a
// local v = c - a
// local w = d - a
let p=-(p0+point);
let mut u=p1-p0;
let mut v=p2-p0;
let w=p3-p0;
// local uv = u:Cross(v)
// local vw = v:Cross(w)
// local wu = w:Cross(u)
// local uvw = uv:Dot(w)
// local pvw = vw:Dot(p)
// local upw = wu:Dot(p)
// local uvp = uv:Dot(p)
let mut uv=u.cross(v);
let vw=v.cross(w);
let wu=w.cross(u);
let uv_w=uv.dot(w);
let pv_w=vw.dot(p);
let up_w=wu.dot(p);
let uv_p=uv.dot(p);
// if pvw/uvw >= 0 and upw/uvw >= 0 and uvp/uvw >= 0 then
if !pv_w.div_sign(uv_w).is_negative()
||!up_w.div_sign(uv_w).is_negative()
||!uv_p.div_sign(uv_w).is_negative(){
// origin is contained, this is a positive detection
// local direction = Vector3.new(0, 0, 0)
// return direction, a0, a1, b0, b1, c0, c1, d0, d1
return Reduce::Escape([v0,v1,v2,v3]);
}
// local uvwSign = uvw < 0 and -1 or uvw > 0 and 1 or 0
// local uvDist = uvp*uvwSign/uv.magnitude
// local vwDist = pvw*uvwSign/vw.magnitude
// local wuDist = upw*uvwSign/wu.magnitude
// local minDist3 = math.min(uvDist, vwDist, wuDist)
let uv_dist=uv_p.mul_sign(uv_w);
let vw_dist=pv_w.mul_sign(uv_w);
let wu_dist=up_w.mul_sign(uv_w);
let wu_len=wu.length();
let uv_len=uv.length();
let vw_len=vw.length();
if vw_dist*wu_len<wu_dist*vw_len{
// if vwDist == minDist3 then
if vw_dist*uv_len<uv_dist*vw_len{
(u,v)=(v,w);
uv=vw;
// uv_p=pv_w; // unused
// b0, c0 = c0, d0
// b1, c1 = c1, d1
(v1,v2)=(v2,v3);
}else{
v2=v3;
}
}else{
// elseif wuDist == minDist3 then
if wu_dist*uv_len<uv_dist*wu_len{
(u,v)=(w,u);
uv=wu;
// uv_p=up_w; // unused
// b0, c0 = d0, b0
// b1, c1 = d1, b1
// before [a,b,c,d]
(v1,v2)=(v3,v1);
// after [a,d,b]
}else{
v2=v3;
}
}
// local up = u:Cross(p)
// local pv = p:Cross(v)
// local uv_up = uv:Dot(up)
// local uv_pv = uv:Dot(pv)
let mut up=u.cross(p);
let pv=p.cross(v);
let uv_up=uv.dot(up);
let uv_pv=uv.dot(pv);
// if uv_up >= 0 and uv_pv >= 0 then
if !uv_up.is_negative()&&!uv_pv.is_negative(){
// local direction = uvw < 0 and uv or -uv
// return direction, a0, a1, b0, b1, c0, c1
if uv_w.is_negative(){
return Reduce::Reduced(Reduced{
dir:uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex3([v0,v1,v2]),
});
}else{
return Reduce::Reduced(Reduced{
dir:-uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex3([v0,v1,v2]),
});
}
}
// local u_u = u:Dot(u)
// local v_v = v:Dot(v)
// local uDist = uv_up/(u_u*v.magnitude)
// local vDist = uv_pv/(v_v*u.magnitude)
// local minDist2 = math.min(uDist, vDist)
let u_dist=uv_up*v.length();
let v_dist=uv_pv*u.length();
// if vDist == minDist2 then
if v_dist<u_dist{
u=v;
up=-pv;
uv=-uv;
// b0 = c0
// b1 = c1
v1=v2;
}
// local p_u = p:Dot(u)
let p_u=p.dot(u);
// if p_u >= 0 then
if !p_u.is_negative(){
// local direction = up:Cross(u)
let direction=up.cross(u);
// if direction.magnitude == 0 then
if direction==vec3::zero(){
// direction = uvw < 0 and uv or -uv
// return direction, a0, a1, b0, b1
if uv_w.is_negative(){
return Reduce::Reduced(Reduced{
dir:uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
});
}else{
return Reduce::Reduced(Reduced{
dir:-uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
});
}
}
// return direction, a0, a1, b0, b1
return Reduce::Reduced(Reduced{
dir:direction.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex2([v0,v1]),
});
}
// local direction = p
let dir=p;
// if direction.magnitude == 0 then
if dir==vec3::zero(){
// direction = uvw < 0 and uv or -uv
if uv_w.is_negative(){
return Reduce::Reduced(Reduced{
dir:uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex1([v0]),
});
}else{
return Reduce::Reduced(Reduced{
dir:-uv.narrow_1().unwrap(),
simplex:Simplex1_3::Simplex1([v0]),
});
}
}
// return direction, a0, a1
Reduce::Reduced(Reduced{
dir,
simplex:Simplex1_3::Simplex1([v0]),
})
}
struct Reduced{
dir:Planar64Vec3,
simplex:Simplex1_3,
}
enum Reduce{
Escape(Simplex<4>),
Reduced(Reduced),
}
impl Simplex2_4{
fn reduce(self,mesh:&MinkowskiMesh,point:Planar64Vec3)->Reduce{
match self{
Self::Simplex2(simplex)=>Reduce::Reduced(reduce2(simplex,mesh,point)),
Self::Simplex3(simplex)=>Reduce::Reduced(reduce3(simplex,mesh,point)),
Self::Simplex4(simplex)=>reduce4(simplex,mesh,point),
}
}
}
pub fn contains_point(mesh:&MinkowskiMesh,point:Planar64Vec3)->bool{
const ENABLE_FAST_FAIL:bool=true;
// TODO: remove mesh negation
minimum_difference::<ENABLE_FAST_FAIL,_>(&-mesh,point,
// on_exact
|is_intersecting,_simplex|{
is_intersecting
},
// on_escape
|_simplex|{
// intersection is guaranteed at this point
true
},
// fast_fail value
||false
)
}
//infinity fev algorithm state transition
#[derive(Debug)]
enum Transition{
Done,//found closest vert, no edges are better
Vert(MinkowskiVert),//transition to vert
}
enum EV{
Vert(MinkowskiVert),
Edge(crate::model::MinkowskiEdge),
}
impl MinkowskiMesh<'_>{
fn next_transition_vert(&self,vert_id:MinkowskiVert,best_distance_squared:&mut Fixed<2,64>,point:Planar64Vec3)->Transition{
let mut best_transition=Transition::Done;
for &directed_edge_id in self.vert_edges(vert_id).as_ref(){
//is boundary uncrossable by a crawl from infinity
let edge_verts=self.edge_verts(directed_edge_id.as_undirected());
//select opposite vertex
let test_vert_id=edge_verts.as_ref()[directed_edge_id.parity() as usize];
//test if it's closer
let diff=point-self.vert(test_vert_id);
let distance_squared=diff.dot(diff);
if distance_squared<*best_distance_squared{
best_transition=Transition::Vert(test_vert_id);
*best_distance_squared=distance_squared;
}
}
best_transition
}
fn final_ev(&self,vert_id:MinkowskiVert,best_distance_squared:&mut Fixed<2,64>,point:Planar64Vec3)->EV{
let mut best_transition=EV::Vert(vert_id);
let diff=point-self.vert(vert_id);
for &directed_edge_id in self.vert_edges(vert_id).as_ref(){
let edge_n=self.directed_edge_n(directed_edge_id);
//is boundary uncrossable by a crawl from infinity
//check if time of collision is outside Time::MIN..Time::MAX
let d=edge_n.dot(diff);
//test the edge
let edge_nn=edge_n.dot(edge_n);
if !d.is_negative()&&d<=edge_nn{
let distance_squared={
let c=diff.cross(edge_n);
//wrap for speed
(c.dot(c)/edge_nn).divide().wrap_2()
};
if distance_squared<=*best_distance_squared{
best_transition=EV::Edge(directed_edge_id.as_undirected());
*best_distance_squared=distance_squared;
}
}
}
best_transition
}
fn crawl_boundaries(&self,mut vert_id:MinkowskiVert,mut best_distance_squared:Fixed<2,64>,point:Planar64Vec3)->EV{
loop{
match self.next_transition_vert(vert_id,&mut best_distance_squared,point){
Transition::Done=>return self.final_ev(vert_id,&mut best_distance_squared,point),
Transition::Vert(new_vert_id)=>vert_id=new_vert_id,
}
}
}
/// This function drops a vertex down to an edge or a face if the path from infinity did not cross any vertex-edge boundaries but the point is supposed to have already crossed a boundary down from a vertex
fn crawl_to_closest_fev(&self,simplex:Simplex<3>,point:Planar64Vec3)->FEV::<Self>{
let (vert_id,best_distance_squared)=simplex.into_iter().map(|vert_id|{
let diff=point-self.vert(vert_id);
(vert_id,diff.dot(diff))
}).min_by_key(|&(_,d)|d).unwrap();
//start on any vertex
//cross uncrossable vertex-edge boundaries until you find the closest vertex or edge
//cross edge-face boundary if it's uncrossable
match self.crawl_boundaries(vert_id,best_distance_squared,point){
//if a vert is returned, it is the closest point to the infinity point
EV::Vert(vert_id)=>FEV::Vert(vert_id),
EV::Edge(edge_id)=>{
//cross to face if the boundary is not crossable and we are on the wrong side
let edge_n=self.edge_n(edge_id);
// point is multiplied by two because vert_sum sums two vertices.
let delta_pos=point*2-{
let &[v0,v1]=self.edge_verts(edge_id).as_ref();
self.vert(v0)+self.vert(v1)
};
for (i,&face_id) in self.edge_faces(edge_id).as_ref().iter().enumerate(){
let face_n=self.face_nd(face_id).0;
//edge-face boundary nd, n facing out of the face towards the edge
let boundary_n=face_n.cross(edge_n)*(i as i64*2-1);
let boundary_d=boundary_n.dot(delta_pos);
//check if time of collision is outside Time::MIN..Time::MAX
//infinity_dir can always be treated as a velocity
if !boundary_d.is_positive(){
//both faces cannot pass this condition, return early if one does.
return FEV::Face(face_id);
}
}
FEV::Edge(edge_id)
},
}
}
}
#[derive(Debug)]
pub struct OhNoes;
pub fn closest_fev_not_inside<'a>(mesh:&MinkowskiMesh<'a>,point:Planar64Vec3)->Option<Result<FEV<MinkowskiMesh<'a>>,OhNoes>>{
const ENABLE_FAST_FAIL:bool=false;
// TODO: remove mesh negation
minimum_difference::<ENABLE_FAST_FAIL,_>(&-mesh,point,
// on_exact
|is_intersecting,simplex|{
if is_intersecting{
return None;
}
// Convert simplex to FEV
// Vertices must be inverted since the mesh is inverted
Some(match simplex{
Simplex1_3::Simplex1([v0])=>Ok(FEV::Vert(-v0)),
Simplex1_3::Simplex2([v0,v1])=>{
// invert
let (v0,v1)=(-v0,-v1);
// TODO: handle non-canonnical multi-edge spanning edges
// dumbest stupidest brute force search
let v0e=mesh.vert_edges(v0);
for &v0e in v0e.as_ref(){
// check opposite vertex to see if it is v1
if mesh.edge_verts(v0e.as_undirected()).as_ref()[v0e.parity() as usize]==v1{
return Some(Ok(FEV::Edge(v0e.as_undirected())));
}
}
Err(OhNoes)
},
Simplex1_3::Simplex3([v0,v1,v2])=>{
// invert
let (v0,v1,v2)=(-v0,-v1,-v2);
let p0=mesh.vert(v0);
let p1=mesh.vert(v1);
let p2=mesh.vert(v2);
// spanning simplex normal
let n=(p2-p0).cross(p1-p0);
// Scan opposite vertices for coplanar ones and find a coplanar face
for &v0e in mesh.vert_edges(v0).as_ref(){
// check if opposite vertex is coplanar
let o0=mesh.edge_verts(v0e.as_undirected()).as_ref()[v0e.parity() as usize];
let o0p=mesh.vert(o0);
if n.dot(o0p-p0).is_zero(){
// always take left face (or right idk just use the parity)
let f0=mesh.edge_faces(v0e.as_undirected()).as_ref()[v0e.parity() as usize];
{
}
}
}
// Shimmy to the side until you find a face that contains the closest point
Err(OhNoes)
},
})
},
// on_escape
|_simplex|{
// intersection is guaranteed at this point
// local norm, dist, u0, u1, v0, v1, w0, w1 = expand(queryP, queryQ, a0, a1, b0, b1, c0, c1, d0, d1, 1e-5)
// let simplex=refine_to_exact(mesh,simplex);
None
},
// fast_fail value is irrelevant and will never be returned!
||unreachable!()
)
}
// local function minimumDifference(
// queryP, radiusP,
// queryQ, radiusQ,
// exitRadius, testIntersection
// )
fn minimum_difference<const ENABLE_FAST_FAIL:bool,T>(
mesh:&MinkowskiMesh,
point:Planar64Vec3,
on_exact:impl FnOnce(bool,Simplex1_3)->T,
on_escape:impl FnOnce(Simplex<4>)->T,
on_fast_fail:impl FnOnce()->T,
)->T{
// local initialAxis = queryQ() - queryP()
// local new_point_p = queryP(initialAxis)
// local new_point_q = queryQ(-initialAxis)
// local direction, a0, a1, b0, b1, c0, c1, d0, d1
let mut initial_axis=mesh.hint_point()+point;
// degenerate case
if initial_axis==vec3::zero(){
initial_axis=choose_any_direction();
}
let last_point=mesh.farthest_vert(-initial_axis);
// this represents the 'a' value in the commented code
let mut last_pos=mesh.vert(last_point);
let Reduced{dir:mut direction,simplex:mut simplex_small}=reduce1([last_point],mesh,point);
// exitRadius = testIntersection and 0 or exitRadius or 1/0
// for _ = 1, 100 do
loop{
// new_point_p = queryP(-direction)
// new_point_q = queryQ(direction)
// local next_point = new_point_q - new_point_p
let next_point=mesh.farthest_vert(direction);
let next_pos=mesh.vert(next_point);
// if -direction:Dot(next_point) > (exitRadius + radiusP + radiusQ)*direction.magnitude then
if ENABLE_FAST_FAIL&&direction.dot(next_pos+point).is_negative(){
return on_fast_fail();
}
let simplex_big=simplex_small.push_front(next_point);
// if
// direction:Dot(next_point - a) <= 0 or
// absDet(next_point, a, b, c) < 1e-6
if !direction.dot(next_pos-last_pos).is_positive()
||simplex_big.det_is_zero(mesh){
// Found enough information to compute the exact closest point.
// local norm = direction.unit
// local dist = a:Dot(norm)
// local hits = -dist < radiusP + radiusQ
let is_intersecting=(last_pos+point).dot(direction).is_positive();
return on_exact(is_intersecting,simplex_small);
}
// direction, a0, a1, b0, b1, c0, c1, d0, d1 = reduceSimplex(new_point_p, new_point_q, a0, a1, b0, b1, c0, c1)
match simplex_big.reduce(mesh,point){
// if a and b and c and d then
Reduce::Escape(simplex)=>{
// Enough information to conclude that the meshes are intersecting.
// Topology information is computed if needed.
return on_escape(simplex);
},
Reduce::Reduced(reduced)=>{
direction=reduced.dir;
simplex_small=reduced.simplex;
},
}
// next loop this will be a
last_pos=next_pos;
}
}