jc/math/shape.jai

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Rect :: #type,distinct Vec(4, RECT_TYPE);
Circle :: struct {
x,y,r: float;
#place x;
pos: Vec2;
}
Line :: struct {
x0,y0,x1,y1: float;
#place x0;
a: Vec2;
#place x1;
b: Vec2;
#place x0;
e: [2]Vec2;
}
Triangle :: [3]Vec2;
ORIGIN :: Vec2.{.[0, 0]};
make_rect :: (x: RECT_TYPE, y: RECT_TYPE, w: RECT_TYPE, h: RECT_TYPE) -> Rect {
r: Rect = ---;
r.x = x;
r.y = y;
r.width = w;
r.height = h;
return r;
}
cut_left :: (rect: *Rect, want: RECT_TYPE) -> Rect {
amnt := basic.min(want, rect.width);
r := rect.*;
r.width = amnt;
rect.x += amnt;
rect.width -= amnt;
return r;
}
cut_right :: (rect: *Rect, want: RECT_TYPE) -> Rect {
amnt := basic.min(want, rect.width);
r := rect.*;
r.x += rect.width - amnt;
r.width = amnt;
rect.width -= r.width;
return r;
}
cut_top :: (rect: *Rect, want: RECT_TYPE) -> Rect {
amnt := basic.min(rect.height, want);
r := rect.*;
r.height -= amnt;
rect.y += amnt;
rect.height -= amnt;
return r;
}
cut_bottom :: (rect: *Rect, want: RECT_TYPE) -> Rect {
amnt := basic.min(want, rect.height);
r := rect.*;
r.y += r.height - amnt;
r.height = amnt;
rect.height -= amnt;
return r;
}
area :: (r: Rect) -> float {
return r.width*r.height;
}
area :: (c: Circle) -> float {
return PI*c.r*c.r;
}
inside :: (r: Rect, p: Vec2) -> bool #symmetric {
return p.x >= r.x && p.x <= r.x + r.width &&
p.y >= r.y && p.y <= r.y + r.height;
}
inside :: (c: Circle, p: Vec2) -> bool #symmetric {
dp := p - c.pos;
return dp.x*dp.x + dp.y*dp.y <= c.r*c.r;
}
inside :: (t: Triangle, p: Vec2) -> bool #symmetric {
cay := t[2].y - t[0].y;
pay := p.y - t[0].y;
cax := t[2].x - t[0].x;
bay := t[1].y - t[0].y;
bax := t[1].x - t[0].x;
denom := bay*cax - bax*cay;
w1 := t[0].x*cay + pay*cax - p.x*cay;
w1 /= denom;
w2 := (p.y - t[0].y - w1*bay)/cay;
return w1 >= 0 && w2 >= 0 && w1 + w2 <= 1;
}
collides :: (c1: Circle, c2: Circle) -> bool {
dp := c2.pos - c1.pos;
return c1.r + c2.r >= length(dp);
}
// Note(Jesse): This is using sdfs. Very elegant
collides :: (c: Circle, r: Rect) -> bool #symmetric {
// We need to 'transpose' all the math to the origin the center of the circle acting as the origin (0, 0)
r_center: Vec2 = get_center(r);
p := r_center - c.pos;
d: Vec2 = abs(p) - Vec2.{.[r.width/2, r.height/2]};
dist := length(max(d, 0.0)) + min(max(d.x, d.y), 0.0);
dist -= c.r; // 'adding' the distance of the circle
return dist <= 0.0;
}
// Note(Jesse): Minkowski difference but instead of the origin we check if the other rectangle center
collides :: (r1: Rect, r2: Rect) -> bool {
r: Rect = Rect.{.[r1.x - r2.width/2, r1.y - r2.width/2, r1.width + r2.width, r1.height + r2.height]};
return inside(r, get_center(r2));
}
collides :: (c: Circle, seg: Line) -> bool #symmetric {
pa := c.pos - seg.a;
ba := seg.b - seg.a;
// Note(Jesse): Using clamp here will cause small segments to collide even when they don't
h: float = min(max(dot(pa,ba)/dot(ba,ba), 0.0), 1.0);
dist := length(pa - ba*h);
return dist - c.r <= 0.0;
}
collides :: (s1: Line, s2: Line) -> bool {
denom := ((s2.y1 - s2.y0)*(s1.x1 - s1.x0) - (s2.x1 - s2.x0)*(s1.y1 - s1.y0));
a := ((s2.x1 - s2.x0)*(s1.y0 - s2.y0) - (s2.y1 - s2.y0)*(s1.x0 - s2.x0));
b := ((s1.x1 - s1.x0)*(s1.y0 - s2.y0) - (s1.y1 - s1.y0)*(s1.x0 - s2.x0));
if denom == 0.0
return false;
a /= denom;
b /= denom;
return (a >= 0 && a <= 1) && (b >= 0 && b <= 1);
}
// Cohen-sutherland's line clipping algorithm
collides :: (r: Rect, l: Line) -> bool #symmetric {
INSIDE :: 0b0000;
LEFT :: 0b0001;
RIGHT :: 0b0010;
BOTTOM :: 0b0100;
TOP :: 0b1000;
compute_out_code :: (x: float, y: float) -> int #expand {
code := INSIDE;
if x < xmin
code |= LEFT;
else if x > xmax
code |= RIGHT;
if y < ymin
code |= BOTTOM;
else if y > ymax
code |= TOP;
return code;
}
xmin := r.x;
xmax := r.x + r.width;
ymin := r.y;
ymax := r.y + r.height;
x0 := l.a.x;
y0 := l.a.y;
x1 := l.b.x;
y1 := l.b.y;
oc0 := compute_out_code(l.a.x, l.a.y);
oc1 := compute_out_code(l.b.x, l.b.y);
accept: bool;
while true {
if !(oc0 | oc1) {
accept = true;
break;
}
else if oc0 & oc1 {
break;
}
else {
x, y: float = ---;
oc_out := ifx oc1 > oc0 then oc1 else oc0;
// find intersection point;
// slope = (y1 - y0)/(x1 - x0)
// x = x0 + (1/slope)*(ym - y0), ym is ymin or ymax
// y = y0 + slope*(xm - x0), xm is xmin or xmax
// outcode bit guarantees the denom is non-zero
if oc_out & TOP {
x = x0 + (x1 - x0)*(ymax - y0)/(y1 - y0);
y = ymax;
}
else if oc_out & BOTTOM {
x = x0 + (x1 - x0)*(ymin - y0)/(y1 - y0);
y = ymin;
}
else if oc_out & RIGHT {
y = y0 + (y1 - y0)*(xmax - x0)/(x1 - x0);
x = xmax;
}
else {
y = y0 + (y1 - y0)*(xmin - x0)/(x1 - x0);
x = xmin;
}
// Move outside points to intersection point
if oc_out == oc0 {
x0 = x;
y0 = y;
oc0 = compute_out_code(x0, y0);
}
else {
x1 = x;
y1 = y;
oc1 = compute_out_code(x1, y1);
}
}
}
return accept;
}
// Triangle SDF with the circle position inplace of the origin and a circle expansion of the sdf
collides :: (t: Triangle, c: Circle) -> bool #symmetric {
e0 := t[1] - t[0];
e1 := t[2] - t[1];
e2 := t[0] - t[2];
v0 := c.pos - t[0];
v1 := c.pos - t[1];
v2 := c.pos - t[2];
pq0 := v0 - e0*min(max(dot(v0,e0)/dot(e0,e0), 0.0), 1.0);
pq1 := v1 - e1*min(max(dot(v1,e1)/dot(e1,e1), 0.0), 1.0);
pq2 := v2 - e2*min(max(dot(v2,e2)/dot(e2,e2), 0.0), 1.0);
s := sign(e0.x*e2.y - e0.y*e2.x);
d := min(min(Vec2.{.[dot(pq0,pq0), s*(v0.x*e0.y - v0.y*e0.x)]},
Vec2.{.[dot(pq1,pq1), s*(v1.x*e1.y - v1.y*e1.x)]}),
Vec2.{.[dot(pq2,pq2), s*(v2.x*e2.y - v2.y*e2.x)]});
dist := -math.sqrt(d.x)*sign(d.y);
return dist < c.r;
}
collides :: (t: Triangle, r: Rect) -> bool #symmetric {
p1 := Vec2.{.[r.x, r.y]};
p2 := Vec2.{.[r.x + r.width, r.y]};
p3 := Vec2.{.[r.x, r.y + r.height]};
p4 := Vec2.{.[r.x + r.width, r.y + r.height]};
rt1: Triangle = .[p1, p4, p2];
rt2: Triangle = .[p1, p3, p4];
if collides(t, rt1) || collides(t, rt2)
return true;
return false;
}
collides :: (t1: Triangle, t2: Triangle) -> bool {
return inline gjk(t1, t2);
}
collides :: (t: Triangle, l: Line) -> bool #symmetric {
return inline gjk(t, l.e);
}
// Note(Jesse): 2D
gjk :: (s1: []Vec2, s2: []Vec2) -> bool {
S: Simplex2D;
S.a = gjk_support(s1, s2, s1[0] - s2[0]);
d := -S.a; // This makes a vector from S.a towards the origin (ORIGIN - S.a)
S.points = 1;
while true {
A := gjk_support(s1, s2, d);
if !same_dir(A, d) // If A is even towards the origin. Otherwise there's no way they intersect
return false;
S.points += 1;
S.c = S.b; // we want S.a to be the newest point. S.c is the oldest
S.b = S.a;
S.a = A;
if gjk_do_simplex(*S, *d)
return true;
}
return false;
}
#scope_file
basic :: #import "Basic";
// Used with gjk, not for general use
Simplex2D :: struct {
a,b,c: Vec2;
points: int;
}
// Used with gjk. Simplified for 2D
triple_cross :: inline (a: Vec2, b: Vec2, c: Vec2) -> Vec2 {
// return cross(cross(v3(a, 0), v3(b, 0)), v3(c, 0)).xy;
return Vec2.{.[-a.x*b.y*c.y + a.y*b.x*c.y, a.x*b.y*c.x - a.y*b.x*c.x]};
}
// Sets the direction for the next support function based on the simplex we have and how it's orientated
// to the origin: 0, 0. Because we know which point was added last (S.a) we can deduce directions we don't
// have to check
gjk_do_simplex :: (S: *Simplex2D, dir: *Vec2) -> bool {
if S.points == {
case 2;
AB := S.b - S.a;
AO := -S.a;
if same_dir(AB, AO) {
dir.* = triple_cross(AB, AO, AB);
}
else {
dir.* = AO;
S.points = 1;
}
case 3;
AO := -S.a;
// Because this is 2D, we don't need a large 3 point simplex case, or a 4 point case
AB := S.b - S.a;
AC := S.c - S.a;
abperp := triple_cross(AC, AB, AB);
acperp := triple_cross(AB, AC, AC);
if same_dir(abperp, AO) {
S.points = 2;
dir.* = abperp;
}
else if same_dir(acperp, AO) {
S.b = S.c;
S.points = 2;
dir.* = acperp;
}
else {
return true; // origin must be inside the triangle
}
}
return false;
}
// Returns the vertex furthest along the dir vector for two polygons. We could split it up
// to take something that can't be represented by a list of points, like a circle.
gjk_support :: inline (a: []Vec2, b: []Vec2, dir: Vec2) -> Vec2 {
helper :: (t: []Vec2, dir: Vec2) -> Vec2 {
p := t[0];
best := dot(t[0], dir);
for 1..t.count - 1 {
v := t[it];
if dot(t[it], dir) > best {
best = dot(v, dir);
p = v;
}
}
return p;
}
v := helper(a, dir);
w := helper(b, -dir);
return v - w;
}
///////
// Helpers and operators
get_center :: (r: Rect) -> Vec2 {
return v2f(r.x + r.width/2, r.y + r.height/2);
}
#if #exists(RUN_TESTS) #run {
// Just a formality to get proper compile errors
b: bool;
r1 := Rect.{.[100, 150, 250, 250]};
c1 := Circle.{150, 500, 50};
l1 := Line.{400, 100, 650, 150};
t1: Triangle;
t1[0] = v2f(600.0, 500.0);
t1[1] = v2f(650.0, 250.0);
t1[2] = v2f(625.0, 200.0);
p: Vec2 = v2f(100.0, 100.0);
r2 := Rect.{.[100, 100, 10, 10]};
c2 := Circle.{100, 100, 10};
l2 := Line.{100, 100, 200, 200};
t2: Triangle;
t2[0] = v2f(50.0, 50.0 + 20.0);
t2[1] = v2f(50.0 + 20.0, 50.0 - 20.0);
t2[2] = v2f(50.0 - 20.0, 50.0 - 20.0);
b |= inside(r1, p);
b |= collides(r1, r2);
b |= collides(r1, l2);
b |= collides(r1, c2);
b |= collides(r1, t2);
b |= inside(c1, p);
b |= collides(c1, r2);
b |= collides(c1, l2);
b |= collides(c1, c2);
b |= collides(c1, t2);
b |= collides(l1, r2);
b |= collides(l1, l2);
b |= collides(l1, c2);
b |= collides(l1, t2);
b |= inside(t1, p);
b |= collides(t1, r2);
b |= collides(t1, l2);
b |= collides(t1, c2);
b |= collides(t1, t2);
}