#include "common.h"#include <stddef.h>#include <stdio.h>#include <strings.h>#include <math.h>#include "machine.h"#include "vmath.h"#include "db.h"#include "nmg.h"#include "raytrace.h"#include "rtgeom.h"#include "./debug.h"Include dependency graph for g_ehy.c:
Go to the source code of this file.
Data Structures | |
| struct | ehy_specific |
Defines | |
| #define | EHY_NORM_BODY (1) |
| #define | EHY_NORM_TOP (2) |
| #define | RT_EHY_SEG_MISS(SEG) (SEG).seg_stp=RT_SOLTAB_NULL |
Functions | |
| int | rt_ehy_prep (struct soltab *stp, struct rt_db_internal *ip, struct rt_i *rtip) |
| void | rt_ehy_print (register const struct soltab *stp) |
| int | rt_ehy_shot (struct soltab *stp, register struct xray *rp, struct application *ap, struct seg *seghead) |
| void | rt_ehy_vshot (struct soltab **stp, struct xray **rp, struct seg *segp, int n, struct application *ap) |
| void | rt_ehy_norm (register struct hit *hitp, struct soltab *stp, register struct xray *rp) |
| void | rt_ehy_curve (register struct curvature *cvp, register struct hit *hitp, struct soltab *stp) |
| void | rt_ehy_uv (struct application *ap, struct soltab *stp, register struct hit *hitp, register struct uvcoord *uvp) |
| void | rt_ehy_free (register struct soltab *stp) |
| int | rt_ehy_class (void) |
| int | rt_ehy_plot (struct bu_list *vhead, struct rt_db_internal *ip, const struct rt_tess_tol *ttol, const struct bn_tol *tol) |
| int | rt_ehy_tess (struct nmgregion **r, struct model *m, struct rt_db_internal *ip, const struct rt_tess_tol *ttol, const struct bn_tol *tol) |
| int | rt_ehy_import (struct rt_db_internal *ip, const struct bu_external *ep, register const fastf_t *mat, const struct db_i *dbip) |
| int | rt_ehy_export (struct bu_external *ep, const struct rt_db_internal *ip, double local2mm, const struct db_i *dbip) |
| int | rt_ehy_import5 (struct rt_db_internal *ip, const struct bu_external *ep, register const fastf_t *mat, const struct db_i *dbip) |
| int | rt_ehy_export5 (struct bu_external *ep, const struct rt_db_internal *ip, double local2mm, const struct db_i *dbip) |
| int | rt_ehy_describe (struct bu_vls *str, const struct rt_db_internal *ip, int verbose, double mm2local) |
| void | rt_ehy_ifree (struct rt_db_internal *ip) |
Variables | |
| const struct bu_structparse | rt_ehy_parse [] |
Algorithm -
Given V, H, R, and B, there is a set of points on this ehy
{ (x,y,z) | (x,y,z) is on ehy }
Through a series of Affine Transformations, this set of points will be transformed into a set of points on an ehy located at the origin with a semi-major axis R1 along the +Y axis, a semi-minor axis R2 along the -X axis, a height H along the -Z axis, a vertex V at the origin, and a distance c between the tip of the hyperboloid and vertex of the asymptotic cone.
{ (x',y',z') | (x',y',z') is on ehy at origin }
The transformation from X to X' is accomplished by:
X' = S(R( X - V ))
where R(X) = ( R2/(-|R2|) ) ( R1/( |R1|) ) . X ( H /(-|H |) )
and S(X) = ( 1/|R2| 0 0 ) ( 0 1/|R1| 0 ) . X ( 0 0 1/|H | )
To find the intersection of a line with the surface of the ehy, consider the parametric line L:
L : { P(n) | P + t(n) . D }
Call W the actual point of intersection between L and the ehy. Let W' be the point of intersection between L' and the unit ehy.
L' : { P'(n) | P' + t(n) . D' }
W = invR( invS( W' ) ) + V
Where W' = k D' + P'.
If Dy' and Dz' are both 0, then there is no hit on the ehy; but the end plates need checking. If there is now only 1 hit point, the top plate needs to be checked as well.
Line L' hits the infinitely long canonical ehy at W' when
A * k**2 + B * k + C = 0
where
A = Dz'**2 - (2*c' + 1)*(Dx'**2 + Dy'**2) B = 2*( (Pz' + c' + 1)*Dz' - (2*c' + 1)*(Dx'*Px' + Dy'Py') ) C = Pz'**2 - (2*c' + 1)*(Px'**2 + Py'**2 - 1) + 2*(c' + 1)*Pz' b = |Breadth| = 1.0 h = |Height| = 1.0 r = 1.0 c' = c / |Breadth|
The quadratic formula yields k (which is constant):
k = [ -B +/- sqrt( B**2 - 4 * A * C )] / (2.0 * A)
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 canonical ehy IFF -1 <= Wz' <= 0.
NORMALS. Given the point W on the surface of the ehy, what is the vector normal to the tangent plane at that point?
Map W onto the unit ehy, ie: W' = S( R( W - V ) ).
Plane on unit ehy at W' has a normal vector N' where
N' = <Wx', Wy', -(z + c + 1) / (2*c + 1)>
The plane transforms back to the tangent plane at W, and this new plane (on the original ehy) has a normal vector of N, viz:
N = inverse[ transpose( inverse[ S o R ] ) ] ( N' )
because if H is perpendicular to plane Q, and matrix M maps from Q to Q', then inverse[ transpose(M) ] (H) is perpendicular to Q'. Here, H and Q are in "prime space" with the unit sphere. [Somehow, the notation here is backwards]. So, the mapping matrix M = inverse( S o R ), because S o R maps from normal space to the unit sphere.
N = inverse[ transpose( inverse[ S o R ] ) ] ( N' ) = inverse[ transpose(invR o invS) ] ( N' ) = inverse[ transpose(invS) o transpose(invR) ] ( N' ) = inverse[ inverse(S) o R ] ( N' ) = invR o S ( N' )
because inverse(R) = transpose(R), so R = transpose( invR ), and S = transpose( S ).
Note that the normal vector produced above will not have unit length.
THE TOP PLATE.
If Dz' == 0, line L' is parallel to the top plate, so there is no hit on the top plate. Otherwise, rays intersect the top plate with k = (0 - Pz')/Dz'. The solution is within the top plate IFF Wx'**2 + Wy'**2 <= 1.
The normal for a hit on the top plate is -Hunit.
Authors - Michael J. Markowski
Source - SECAD/VLD Computing Consortium, Bldg 394 The U. S. Army Ballistic Research Laboratory Aberdeen Proving Ground, Maryland 21005-5066
Definition in file g_ehy.c.
1.4.6