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#ifndef SURFACE_H
#define SURFACE_H
#include "fml.h"
#include "manifold.h"
namespace fml {
/* All surfaces inherit this class */
/* The exact meaning of d is surface-dependent (see class
* definitions below); the limit of the calculated integral must
* approach its true value as d->0. d must be > 0. */
class Surface : public Manifold {
public:
const int dimension() const { return 2; }
};
class Plane : public Surface {
private:
/* The surface is specified by all points p = p0 + s v1 + t v2,
* such that 0 <= {s, t} < 1
*
* v1 and v2 must NOT be parallel.
*
* v1 and v2 should (but do not have to be) be normal (this is
* motivated primarily by usability; if the two vectors are indeed
* normal, then m1 and m2 have the nice geometric meaning of side
* length).
*
* d = ds = dt.
* dA will be in the direction of v1 x v2.
*/
vec3 p0, v1, v2;
public:
Plane(vec3 p, vec3 _v1, vec3 _v2) : p0(p), v1(_v1), v2(_v2) {};
vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
const char *name() const { return "Plane"; }
};
/* Flat, circular disk (of varying extent) */
class Disk : public Surface {
private:
/* This represents a (possibly incomplete) circular disk in space,
* with a center, radius, and normal vector as specified.
*
* `angle' specifies the extent of the disk; angle=2pi for a full
* circle.
*
* We use:
* d = dr.
* d_theta = d / r.
*
* This makes it so that differential area elements on the edge of
* the disk are square.
*
* dA will be in the direction of normal.
*/
vec3 center, radius, normal;
scalar angle;
public:
Disk(vec3 c, vec3 r, vec3 n, scalar a) : center(c), radius(r), normal(n), angle(a) {};
vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
const char *name() const { return "Disk"; }
};
/* Hollow, spherical shell */
class Sphere : public Surface {
private:
/* d = dtheta = dphi */
vec3 center;
scalar radius;
public:
Sphere(vec3 c, scalar r) : center(c), radius(r) {};
vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
const char *name() const { return "Sphere"; }
};
/* Cylinder without end caps */
class OpenCylinder : public Surface {
private:
/* Like this:
*
* ___________________
* / \ \
* origin ---------------> axis
* \_/_________________/
*
*/
vec3 origin, axis;
scalar radius;
public:
OpenCylinder(vec3 o, vec3 a, scalar r) : origin(o), axis(a), radius(r) {}
vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
const char *name() const { return "OpenCylinder"; }
};
/* Capped cylinder */
class ClosedCylinder : public OpenCylinder {
private:
Disk cap1, cap2;
public:
ClosedCylinder(vec3 o, vec3 a, scalar r) : OpenCylinder(o, a, r),
cap1(o, vec3::any_unit_normal(a), -a.normalize(), 2*M_PI),
cap2(o + a, vec3::any_unit_normal(a), a.normalize(), 2*M_PI) {}
vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
const char *name() const { return "ClosedCylinder"; }
};
}
#endif
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