V3D - Volumetric 3D Modeling

Summary

The v3d routines, v3d.sl (version 1.0.0) provide a way to define and visualize 3D cubes of scalar values, with application to volume-filling geometries. Docmentation on the routines are available in the comments in v3d.sl and in this v3d Command Reference web document. The v3d routines described here are basic building blocks and can be used in a variety of contexts.

In an astrophysical modeling context, the scalar values in the 3D array can represent a local physical quantity that gives rise to observed emission, e.g., for thermal X-rays the product n_e*n_i.

Examples of using v3d routines in (i) a front-end for Chandra's MARX simulator, (ii) a custom isis model, (iii) and with a more complex system are given here:

• MARX - S-Lang User model
• ____
• Source-3D and Event-2D

The remainder of this page provides examples of the v3d routines and their capabilities.

An Astrophysical Geometry Example The 20-year-old supernova remnant, SNR 1987A, is made up of several geometric components as shown here in solid cross-section (left) and projected on the sky (right.) These include: the expanding SN ejecta (purple), the dense ``inner ring'' with protrusions (red), the torus-like HII region around the ring (green) and an expanding blastwave out of the equatorial plane (blue). The images were created with the commands in: v3dex_snr1987a.sl

v3d_view, uses volview()

v3d_project, uses imdisplay()

Monte Carlo ``events'' with Doppler Effects

Routines are provided to generate Monte Carlo (MC) samples from a v3d volume array with the probability of the event proportional to the values of the array cell. The set of 3D locations, ``points'', created can be used as input to a ray-trace code. A routine is provided to calculate Line-of-sight Doppler shifts (photon energy factors) based on a velocity field for the points.

The v3d routines also provide a primative event-imaging capapility which can show the events color-coded by the Doppler velocity. The simple examples below were made with the commands in v3dex_mc_vels.sl.

	Solid 3D view	MC events on sky
vtype=0 const*r_hat	vtype=1 const*r_vec	vtype=2 rigid rotation |v| ~ r	vtype=3 Kepler rotation |v| ~ 1/sqrt(r)

Some other examples...

Some other example images and the files used to create them are given here:

Hydra A model v3dex_HydraA.sl

Mystery object v3dex_myst06.sl

SNR E0102, Ne X v3dex_e0102.sl

Basic V3D Routines

Below are examples of some basic shapes available in the v3d.sl routines; these examples were made with the code-snippets indicated and given in full in v3d_shape_demo.sl .
v3d_sphere

v3d_sphere(20.0, 40.0, [20.,40.,20.]) + v3d_sphere(0.0, 20.0, [0.,0.,-50.0])

v3d_spheroid

v3d_spheroid(40.0, 50.0, 1.8, ,[-20.0,70.])

v3d_cylinder

v3d_cylinder(10.0,20.0, 0.0,80.0, , [290.0,0.0]) + v3d_cylinder(40.0, 90.0, -10.0, 10.0, ,[-55.0, -30.0])

v3d_cone

v3d_cone(20.0, 30.0, 30.0, 80.0, , [-40.,-10.]) + 2.0* v3d_cone(0.0, 3.0, -200.0,200.0, , [50.0,60.0] )

v3d_torus

( v3d_torus(30.0,70.0, [20.0,0.,0.],[-40.,10.0]) - v3d_torus(45.0,55.0, [20.,0.,0.], [-40.,10.0]) ) + v3d_torus(30.0,50.0, [-10.,0.,40.], [140.0,80.0])

v3d_cube-slice

v3d_cube(100.0,[-70.,0.,-100.]) * v3d_sphere(50.0,80.0)

v3d_roche

v3d_roche(90., 0.333, 1.0, [-75.0,0.,.0],[0.0,0.0]) + ( v3d_roche(90., 3.0, 1.0, [15.0,0.,0.0],[180.0,0.0]) - v3d_sphere(0.0, 20.0, [15.0,0.,0.0]) )

v3d_sphere_ring

v3d_sphere_ring(70.0, 5.0, 17, , [260.0, -44.0])

v3d_sphere_rlup

v3d_sphere_rlup(1.0,90.0, [0.0,3.0,10.0,30.0,100.0], [10.0,5.0,1.0,3.0,0.5])

v3d_cyl_azlup

v3d_cyl_azlup (70.0, 90.0, -40.0, 40.0, , [-70.0,30.0], azlups,vlups) with: azlups = 9.0*[-10:20:1]; vlups = 0.3 + cos(5.0*azlups*PI/180.0)^2;

v3d_2dto3d

v3d_2dto3d(arr2d, 20.0, 90.0, , [-20.0, 30.0]) with arr2d = Float_Type [91,100]; % from 0 to 10 degrees: 1/5 radius: arr2d[[0:9],[0:20]] = 1.0; % from 10 to 45 degrees: 1/2 radius: arr2d[[10:45],[0:49]] = 1.0; % from 46 to 90 degrees: full radius: arr2d[[46:90],*] = 1.0;

v3d_2dto3d-RT-hydro

v3d_2dto3d(arrRT, 22.0, 90.0, , [90.0,80.0]) with: arr2d = h5_read("wrbub_1026.h5"); ...etc...

v3d_r3dsq

10.0*(1./30.0^3)* exp(-1.0*v3d_r3dsq([0.,0.,0.]) /(30.0^2)) + (1./10.^3)* exp(-1.0* v3d_r3dsq([60.,50.,30.]) /(10.0^2))

v3d_f_generic

v3d_f_generic("custom function", , [-25.0,15.0]) Here, values = (cos(3.0*azimuth))^2 * (sin(5.0*lattitude))^2 * exp(-1.0*rad3dsq/(40.0)^2);