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When I attempted to render the gravitation equipotential surface of two
bodies (i.e the surfaces of the double planet in Robert Forward's
"Flight of the Dragonfly"). The iso_surface object behaved oddly with
these three behaviors:
1) If the contained_by shape is larger than the true surface for the
given threshold value, the entire contained_by shape (either box or
sphere) is rendered as part of the surface.
2) If parts of the surface extend beyond the contained_by shape, you get
the difference of the contained_by shape and the true surface. (this is
shown in POVRay Example 1 below)
3) If the contained_by shape is made large enough to contain the true
surface, camera, and light_source, you get the correct results for the
iso_surface, but it takes a long time to render since every point in the
scene has to be tested.
Since the Gravitational potential is a function of 1/r the function used
is 1/sqrt(x*x+y*y+z*z)
To test where this behavior originates, I did 3 other test files (shown
in Examples 2, 3, and 4 below) which should have all produced the same
result, a sphere of radius 4.47214 (i.e. sqrt(20.0)), with the following
results
Example 2: the function was x*x+y*y+z*z, threshold 20.0
Result: Worked with the proper max_gradient
Example 3: the function was sqrt(x*x+y*y+z*z), threshold 4.47214
Result: Worked with the proper max_gradient
Example 4: the function was 1/(sqrt(x*x+y*y+z*z)+0.0001), threshold 0.22361
Result: Behavior like Example 1, regardless of max_gradient, in fact for
the case where the contained_by shape is larger than the expected
surface, random values of max_gradient make no difference and no value
is printed in the messages so the test of the function is apparently not
taking place.
I've tested this with both linux and Windows versions of POVRay 3.5 with
the same results so it appears to be something pathological in the code
when the function involves 1/sqrt. Does anyone have any insight into this?
Richard Kline
//Begin Example 1
#include "shapes.inc"
#include "shapes2.inc"
#include "colors.inc"
#include "textures.inc"
camera {
location <0.0, 120.0, -75.0>
up < 0.0, 1.0, 0.0>
right < 4/3, 0.0, 0.0>
look_at <5,30.0,0>
angle 60
}
light_source { <25.0, 200.0, -80.0> color White}
#declare Roche = function {
10.0/(sqrt(x*x+y*y+z*z)+0.000001) +
10.0/(sqrt((x+20)*(x+20)+y*y+z*z)+0.000001)}
plane { y,-20
pigment { hexagon pigment {Red}, pigment {Gray50}, pigment {Blue} scale 10}
}
isosurface {
function { Roche(x,y,z) }
contained_by { box {<-15,-5,-5>,<-5,5,5>} }
threshold 2.0
max_gradient 84
texture {pigment {Green} finish {Dull}}
scale <4.5,4.5,4.5>
translate <30,25,0>
// Rotations to show the difference shape
rotate <0,90,0>
rotate <30,0,0>
}
//End Example 1
//Begin Example 2
#include "shapes.inc"
#include "shapes2.inc"
#include "colors.inc"
#include "textures.inc"
camera {
location <0.0, 120.0, -75.0>
up < 0.0, 1.0, 0.0>
right < 4/3, 0.0, 0.0>
look_at <5,30.0,0>
angle 60
}
light_source { <25.0, 200.0, -80.0> color White}
#declare Sphere1 = function {
x*x + y*y + z*z }
plane { y,-20
pigment { hexagon pigment {Red}, pigment {Gray50}, pigment {Blue} scale 10}
}
isosurface {
function {Sphere1(x,y,z)}
contained_by { box {<-6,-6,-6>,<6,6,6>}}
threshold 20.0
max_gradient 16.0
texture {pigment {Green} finish {Dull}}
scale <4.5,4.5,4.5>
}
//End Example 2
//Begin Example 3
#include "shapes.inc"
#include "shapes2.inc"
#include "colors.inc"
#include "textures.inc"
camera {
location <0.0, 120.0, -75.0>
up < 0.0, 1.0, 0.0>
right < 4/3, 0.0, 0.0>
look_at <5,30.0,0>
angle 60
}
light_source { <25.0, 200.0, -80.0> color White}
#declare Sphere2 = function {
sqrt(x*x + y*y + z*z) }
plane { y,-20
pigment { hexagon pigment {Red}, pigment {Gray50}, pigment {Blue} scale 10}
}
isosurface {
function {Sphere2(x,y,z)}
contained_by { box {<-6,-6,-6>,<6,6,6>}}
threshold 4.47214
max_gradient 1.0
texture {pigment {Green} finish {Dull}}
scale <4.5,4.5,4.5>
}
//End Example 3
//Begin Example 4
#include "shapes.inc"
#include "shapes2.inc"
#include "colors.inc"
#include "textures.inc"
camera {
location <0.0, 120.0, -75.0>
up < 0.0, 1.0, 0.0>
right < 4/3, 0.0, 0.0>
look_at <5,30.0,0>
angle 60
}
light_source { <25.0, 200.0, -80.0> color White}
//The +0.0001 in the denominator of the function is to ensure no
// possibility of a divide by zero occurring
#declare Sphere3 = function {
1.0/(sqrt(x*x + y*y + z*z)+0.0001) }
plane { y,-20
pigment { hexagon pigment {Red}, pigment {Gray50}, pigment {Blue} scale 10}
}
isosurface {
function {Sphere3(x,y,z)}
contained_by { box {<-6,-6,-6>,<6,6,6>}}
threshold 0.22361
max_gradient 100.0
texture {pigment {Green} finish {Dull}}
scale <4.5,4.5,4.5>
}
//End Example 4
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