Primitive Collision Detecting (3)

王朝other·作者佚名  2006-05-16
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2D Point In Triangle

See 2D Point In 2D Convex Polygon when n=3

2D Point In Rectangle

Point : P

Rectangle: R { V2d inf, sup;} (inf->infimum, sup->supremum)

if ( P.x >= R.inf.x && P.x <= R.sup.x

&& P.y >= R.inf.y && P.y <= R.sup.y )

{

return Inside;

}

return Outside;

2D Point In ORectangle(Oriented Rectangle, not axis aligned Rectangle)

See 2D Point In 2D Convex Polygon when n=4

Point In Circle Or Sphere

Point : P

Sphere : | P – C | = R (R>=0)

if ( CP * CP <= R^2 )

{

return Inside;

}

return Outside;

2D Point In Ellipse

Point : P

Ellipse: (x - x0)^2 / a^2 + (y - y0)^2 / b^2 = 1 (a>0, b>0)

if ( (P.x-x0)^2 / a^2 + (P.y - y0)^2 / b^2 <= 1 )

{

return Inside;

}

return Outside;

Point In OBB

See 3D Point In Convex Polyhedron when n = 6

Line Segment & Ellipse

Line Seg: P = P0 + t * V (t>=0 && t<=1)

Ellipse : (x - x0)^2 / a^2 + (y - y0)^2 / b^2 = 1 (a>0, b>0)

(P0.x – x0 + t * V.x)^2 / a^2 + (P0.y - y0 + t * V.y)^2 / b^2 = 1

(b^2 * V.x^2 + a^2 * V.y^2) * t^2 + (2 * b^2 * V.x * (P0.x – x0) + 2 * a^2 * V.y * (P0.y – y0)) * t + b^2 * V.x^2 * (P0.x – x0)^2 + a^2 * V.y^2 * (P0.y – y0)^2 – a^2 * b^2 = 0

A = (b^2 * V.x^2 + a^2 * V.y^2);

B = (2 * b^2 * V.x * (P0.x – x0) + 2 * a^2 * V.y * (P0.y – y0));

C = b^2 * V.x^2 * (P0.x – x0)^2 + a^2 * V.y^2 * (P0.y – y0)^2 – a^2 * b^2;

Δ= B^2 – 4AC;

if ( Δ < 0 ) return No Intersection;

t = (-B ± sqrt(B^2 – 4AC)) / 2A;

if ( t >= 0 && t <= 1 ) return Intersectant;

Line Segment & Ellipsoid

Line Seg : P = P0 + t * V (t>=0 && t<=1)

Ellipsoid: (x - x0)^2 / a^2 + (y - y0)^2 / b^2 + (z - z0)^2 / c^2= 1 (a>0, b>0, c>0)

(P0.x – x0 + t * V.x)^2 / a^2 + (P0.y - y0 + t * V.y)^2 / b^2 + (P0.z - z0 + t * V.z)^2 / c^2 = 1

……

Δ= B^2 – 4AC;

if ( Δ < 0 ) return No Intersection;

t = (-B ± sqrt(B^2 – 4AC)) / 2A;

if ( t >= 0 && t <= 1 ) return Intersectant;

Point In Ellipsoid

Point : P

Ellipsoid: (x - x0)^2 / a^2 + (y - y0)^2 / b^2 + (z - z0)^2 / c^2= 1 (a>0, b>0, c>0)

if ( (P.x-x0)^2 / a^2 + (P.y - y0)^2 / b^2 + (P.z - z0)^2 / c^2 <= 1 )

{

return Inside;

}

return Outside;

Rectangle & Rectangle

Rectangle: A { V2d inf, sup;}

Rectangle: B { V2d inf, sup;}

if ( A.inf.x > B.sup.x || A.inf.y > B.sup.y

|| A.sup.x < B.inf.x || A.sup.y < B.inf.y )

{

return No Intersection;

}

return Intersectant;

 
 
 
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