g_rec.c File Reference

#include "common.h"
#include <stdio.h>
#include <math.h>
#include "machine.h"
#include "vmath.h"
#include "raytrace.h"
#include "rtgeom.h"
#include "./debug.h"
#include "noalias.h"

Include dependency graph for g_rec.c:

Go to the source code of this file.

Data Structures
struct	rec_specific
Defines
#define	REC_NORM_BODY   (1)
#define	REC_NORM_TOP   (2)
#define	REC_NORM_BOT   (3)
#define	SEG_MISS(SEG)   (SEG).seg_stp=(struct soltab *) 0;
Functions
int	rt_rec_prep (struct soltab *stp, struct rt_db_internal *ip, struct rt_i *rtip)
void	rt_rec_print (register const struct soltab *stp)
int	rt_rec_shot (struct soltab *stp, register struct xray *rp, struct application *ap, struct seg *seghead)
void	rt_rec_vshot (struct soltab **stp, struct xray **rp, struct seg *segp, int n, struct application *ap)
void	rt_rec_norm (register struct hit *hitp, struct soltab *stp, register struct xray *rp)
void	rt_rec_curve (register struct curvature *cvp, register struct hit *hitp, struct soltab *stp)
void	rt_rec_uv (struct application *ap, struct soltab *stp, register struct hit *hitp, register struct uvcoord *uvp)
void	rt_rec_free (struct soltab *stp)
int	rt_rec_class (void)

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Detailed Description

Intersect a ray with a Right Eliptical Cylinder. This is a special (but common) case of the TGC, which is handled separately.

Algorithm -

Given V, H, A, and B, there is a set of points on this cylinder

{ (x,y,z) | (x,y,z) is on cylinder }

Through a series of Affine Transformations, this set of points will be transformed into a set of points on a unit cylinder located at the origin with a radius of 1, and a height of +1 along the +Z axis.

{ (x',y',z') | (x',y',z') is on cylinder at origin }

The transformation from X to X' is accomplished by:

X' = S(R( X - V ))

where R(X) = ( A/(|A|) ) ( B/(|B|) ) . X ( H/(|H|) )

and S(X) = ( 1/|A| 0 0 ) ( 0 1/|B| 0 ) . X ( 0 0 1/|H| )

To find the intersection of a line with the surface of the cylinder, consider the parametric line L:

L : { P(n) | P + t(n) . D }

Call W the actual point of intersection between L and the cylinder. Let W' be the point of intersection between L' and the unit cylinder.

L' : { P'(n) | P' + t(n) . D' }

W = invR( invS( W' ) ) + V

Where W' = k D' + P'.

If Dx' and Dy' are both 0, then there is no hit on the cylinder; but the end plates need checking.

Line L' hits the infinitely tall unit cylinder at W' when

k**2 + b * k + c = 0

where

b = 2 * ( Dx' * Px' + Dy' * Py' ) / ( Dx'**2 + Dy'**2 ) c = ( ( Px'**2 + Py'**2 ) - r**2 ) / ( Dx'**2 + Dy'**2 ) r = 1.0

The qudratic formula yields k (which is constant):

k = [ -b +/- sqrt( b**2 - 4 * c ] / 2.0

Now, D' = S( R( D ) ) and P' = S( R( P - V ) )

Substituting,

W = V + invR( invS[ k *( S( R( D ) ) ) + S( R( P - V ) ) ] ) = V + invR( ( k * R( D ) ) + R( P - V ) ) = V + k * D + P - V = k * D + P

Note that ``k'' is constant, and is the same in the formulations for both W and W'.

The hit at ``k'' is a hit on the height=1 unit cylinder IFF 0 <= Wz' <= 1.

NORMALS. Given the point W on the surface of the cylinder, what is the vector normal to the tangent plane at that point?

Map W onto the unit cylinder, ie: W' = S( R( W - V ) ).

Plane on unit cylinder at W' has a normal vector N' of the same value as W' in x and y, with z set to zero, ie, (Wx', Wy', 0)

The plane transforms back to the tangent plane at W, and this new plane (on the original cylinder) has a normal vector of N, viz:

N = inverse[ transpose(invR o invS) ] ( N' ) = inverse[ transpose(invS) o transpose(invR) ] ( N' ) = inverse[ inverse(S) o R ] ( N' ) = invR o S ( N' )

Note that the normal vector produced above will not have unit length.

THE END PLATES.

If Dz' == 0, line L' is parallel to the end plates, so there is no hit.

Otherwise, the line L' hits the bottom plate with k = (0 - Pz') / Dz', and hits the top plate with k = (1 - Pz') / Dz'.

The solution W' is within the end plate IFF

Wx'**2 + Wy'**2 <= 1.0

The normal for a hit on the bottom plate is -Hunit, and the normal for a hit on the top plate is +Hunit.

Authors - Edwin O. Davisson (Analysis) Michael John Muuss (Programming)

Source - SECAD/VLD Computing Consortium, Bldg 394 The U. S. Army Ballistic Research Laboratory Aberdeen Proving Ground, Maryland 21005

Definition in file g_rec.c.

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