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Mike Bostock
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431
physics/shape.h
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431
physics/shape.h
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// -*- C++ -*-
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#ifndef MBOSTOCK_SHAPE_H
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#define MBOSTOCK_SHAPE_H
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#include "vector.h"
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namespace mbostock {
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class Plane;
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class Sphere;
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/**
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* Represents the projection of a point onto the closest corresponding point
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* on the surface of a shape. A projection is used when the bounding sphere of
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* a particle interpenetrates a shape and, as this constitutes a collision,
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* the sphere center is projected onto the surface of the shape to determine
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* how to move the particle out in response to the collision.
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*
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* When a point is projected onto a surface, the projection includes the
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* surface normal. However, if the point is projected onto a line, the
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* corresponding normal is undefined.
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*
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* Projections define a natural order based on the length of the projection,
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* so that it is convenient to find the shortest projection given a number of
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* candidate projections.
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*/
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class Projection {
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public:
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Projection();
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Projection(const Vector& x, float length);
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Projection(const Vector& x, float length, const Vector& normal);
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/** The location of the projected point on the shape's surface. */
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Vector x;
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/** The distance from the original point to the projected point. */
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float length;
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/** The surface normal at the projected point. */
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Vector normal;
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bool operator<(const Projection& p) const;
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bool operator<=(const Projection& p) const;
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bool operator>(const Projection& p) const;
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bool operator>=(const Projection& p) const;
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};
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/**
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* Represents a shape in three dimensions. Since particles are represented
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* solely as spheres, shapes need only define intersection tests with spheres,
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* and how to project points onto the closest point on the surface of the
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* shape.
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*/
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class Shape {
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public:
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virtual ~Shape() {}
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/** Returns true if the specified sphere intersects with this shape. */
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virtual bool intersects(const Sphere& s) const = 0;
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/**
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* Projects the specified point onto the surface of the shape. The
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* projection specifies the closest point on the surface of the shape to the
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* specified point, the pre-computed length of the projection (the distance
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* between two points), and the surface normal at the projected point, if
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* defined.
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*/
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virtual Projection project(const Vector& x) const = 0;
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};
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/** Represents a sphere using a center point and a radius. */
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class Sphere : public Shape {
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public:
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Sphere();
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Sphere(const Vector& x, float radius);
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/** The center point of the sphere. */
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inline Vector& x() { return x_; }
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inline const Vector& x() const { return x_; }
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/** The radius of the sphere. */
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inline float radius() const { return r_; }
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/** Returns true if the sphere is entirely above the specified plane. */
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bool above(const Plane& p) const;
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/** Returns true if the sphere is entirely below the specified plane. */
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bool below(const Plane& p) const;
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Vector x_;
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float r_;
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float r2_;
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friend class AxisAlignedBox;
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friend class Cylinder;
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friend class LineSegment;
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friend class Plane;
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friend class Triangle;
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};
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/** Represents a line segment using a start point and an end point. */
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class LineSegment : public Shape {
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public:
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LineSegment();
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LineSegment(const Vector& x0, const Vector& x1);
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/** The start point of the line segment. */
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inline const Vector& x0() const { return x0_; }
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/** The end point of the line segment. */
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inline const Vector& x1() const { return x1_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Vector x0_;
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Vector x1_;
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Vector x01_;
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float l2_;
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friend class Cylinder;
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};
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/** Represents a plane using a point on the plane and a normal. */
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class Plane : public Shape {
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public:
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Plane();
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Plane(const Vector& x, const Vector& normal);
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/** A point on the plane. */
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inline const Vector& x() const { return x_; }
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/** The normal. */
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inline const Vector& normal() const { return n_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Vector x_;
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Vector n_;
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friend class Sphere;
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};
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/** Represents a triangle using three coplanar points. */
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class Triangle : public Shape {
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public:
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Triangle();
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Triangle(const Vector& x0, const Vector& x1, const Vector& x2);
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/** The first point of the triangle. */
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inline const Vector& x0() const { return x01_.x0(); }
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/** The second point of the triangle. */
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inline const Vector& x1() const { return x12_.x0(); }
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/** The third point of the triangle. */
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inline const Vector& x2() const { return x20_.x0(); }
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/** The normal of the triangle, using counterclockwise orientation. */
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inline const Vector& normal() const { return p_.normal(); }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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bool contains(const Vector& p) const;
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LineSegment x01_;
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LineSegment x12_;
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LineSegment x20_;
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Plane p_;
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friend class Wedge;
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};
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/** Represents a quad using four coplanar points. */
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class Quad : public Shape {
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public:
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Quad();
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Quad(const Vector& x0, const Vector& x1,
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const Vector& x2, const Vector& x3);
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/** The first point of the quad. */
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inline const Vector& x0() const { return x01_.x0(); }
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/** The second point of the quad. */
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inline const Vector& x1() const { return x12_.x0(); }
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/** The third point of the quad. */
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inline const Vector& x2() const { return x23_.x0(); }
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/** The fourth point of the quad. */
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inline const Vector& x3() const { return x30_.x0(); }
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/** The normal of the quad, using counterclockwise orientation. */
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inline const Vector& normal() const { return p_.normal(); }
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/** The plane of the quad. */
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inline const Plane& plane() const { return p_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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bool contains(const Vector& p) const;
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LineSegment x01_;
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LineSegment x12_;
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LineSegment x23_;
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LineSegment x30_;
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Plane p_;
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friend class Wedge;
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};
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/**
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* Represents a wedge using the four coplanar points of the top surface.
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* Points x1 and x2 define the upper edge of the wedge; points x4 and x5 lie
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* directly beneath them to define the fifth side.
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*/
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class Wedge : public Shape {
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public:
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Wedge();
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Wedge(const Vector& x0, const Vector& x1,
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const Vector& x2, const Vector& x3);
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/** Returns the first (lower) point of the wedge. */
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inline const Vector& x0() const { return top_.x0(); }
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/** Returns the second (upper) point of the wedge. */
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inline const Vector& x1() const { return top_.x1(); }
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/** Returns the third (upper) point of the wedge. */
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inline const Vector& x2() const { return top_.x2(); }
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/** Returns the forth (upper) point of the wedge. */
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inline const Vector& x3() const { return top_.x3(); }
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/** Returns the fifth point of the wedge, below x1. */
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inline const Vector& x4() const { return right_.x2(); }
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/** Returns the six point of the wedge, below x2. */
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inline const Vector& x5() const { return right_.x3(); }
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/** Returns the top quad. */
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inline const Quad& top() const { return top_; }
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/** Returns the right quad. */
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inline const Quad& right() const { return right_; }
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/** Returns the bottom quad. */
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inline const Quad& bottom() const { return bottom_; }
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/** Returns the front triangle. */
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inline const Triangle& front() const { return front_; }
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/** Returns the back triangle. */
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inline const Triangle& back() const { return back_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Quad top_;
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Quad right_;
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Quad bottom_;
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Triangle front_;
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Triangle back_;
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};
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/**
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* Represents an axis-aligned bounding box (AABB) using two points. The min
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* point is the bottom back left point, and the max point is the top front
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* right point.
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*/
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class AxisAlignedBox : public Shape {
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public:
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AxisAlignedBox();
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AxisAlignedBox(const Vector& min, const Vector& max);
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/** Returns the min point, x0. */
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inline const Vector& min() const { return min_; }
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/** Returns the max point, x7. */
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inline const Vector& max() const { return max_; }
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/** Returns the left bottom back point. */
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inline const Vector& x0() const { return min_; }
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/** Returns the right bottom back point. */
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inline Vector x1() const { return Vector(max_.x, min_.y, min_.z); }
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/** Returns the right bottom front point. */
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inline Vector x2() const { return Vector(max_.x, min_.y, max_.z); }
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/** Returns the left bottom front point. */
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inline Vector x3() const { return Vector(min_.x, min_.y, max_.z); }
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/** Returns the right top back point. */
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inline Vector x4() const { return Vector(max_.x, max_.y, min_.z); }
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/** Returns the left top back point. */
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inline Vector x5() const { return Vector(min_.x, max_.y, min_.z); }
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/** Returns the left top front point. */
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inline Vector x6() const { return Vector(min_.x, max_.y, max_.z); }
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/** Returns the right top front point. */
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inline const Vector& x7() const { return max_; }
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/** Returns true if this box contains the specified point. */
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bool contains(const Vector& p) const;
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Projection projectOut(const Vector& p) const;
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Projection projectIn(const Vector& p) const;
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Vector min_;
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Vector max_;
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};
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/**
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* Represents an oriented bounding box (OBB) using eight points.
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*/
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class Box : public Shape {
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public:
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Box();
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Box(const AxisAlignedBox& aab);
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Box(const Vector& c, const Vector& x, const Vector& y, const Vector& z);
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Box(const Vector& x0, const Vector& x1, const Vector& x2, const Vector& x3,
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const Vector& x4, const Vector& x5, const Vector& x6, const Vector& x7);
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/** Returns the left bottom back point. */
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inline const Vector& x0() const { return bottom_.x0(); }
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/** Returns the right bottom back point. */
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inline const Vector& x1() const { return bottom_.x1(); }
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/** Returns the right bottom front point. */
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inline const Vector& x2() const { return bottom_.x2(); }
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/** Returns the left bottom front point. */
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inline const Vector& x3() const { return bottom_.x3(); }
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/** Returns the right top back point. */
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inline const Vector& x4() const { return top_.x0(); }
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/** Returns the left top back point. */
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inline const Vector& x5() const { return top_.x1(); }
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/** Returns the left top front point. */
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inline const Vector& x6() const { return top_.x2(); }
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/** Returns the right top front point. */
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inline const Vector& x7() const { return top_.x3(); }
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/** Returns the left quad. */
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inline const Quad& left() const { return back_; }
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/** Returns the right quad. */
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inline const Quad& right() const { return right_; }
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/** Returns the bottom quad. */
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inline const Quad& bottom() const { return bottom_; }
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/** Returns the top quad. */
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inline const Quad& top() const { return top_; }
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/** Returns the back quad. */
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inline const Quad& back() const { return back_; }
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/** Returns the front quad. */
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inline const Quad& front() const { return front_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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Quad top_;
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Quad bottom_;
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Quad left_;
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Quad right_;
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Quad front_;
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Quad back_;
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};
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/** Represents a cylinder as two points and a radius. */
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class Cylinder : public Shape {
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public:
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Cylinder();
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Cylinder(const Vector& x0, const Vector& x1, float radius);
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/** Returns the start point of the cylinder's main axis. */
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inline const Vector& x0() const { return axis_.x0(); }
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/** Returns the end point of the cylinder's main axis. */
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inline const Vector& x1() const { return axis_.x1(); }
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/** Returns the radius. */
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inline float radius() const { return r_; }
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/** Returns the length of the cylinder. */
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inline float length() const { return l_; }
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/** Returns the unit direction vector of the cylinder. */
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inline const Vector& z() const { return v_; }
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virtual bool intersects(const Sphere& s) const;
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virtual Projection project(const Vector& p) const;
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private:
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LineSegment axis_;
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float l_;
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float r_;
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Vector v_;
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};
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};
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#endif
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