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I get clean fully visible slices.
#version 3.8;
global_settings {assumed_gamma 1.0 }
#include "colors.inc"
#declare Aspect = image_width/image_height;
camera {
location <0, 5, -10>
right x*Aspect
look_at <0, 0, 0>
}
light_source {<0, 5, -10> color White}
plane {z, 1 pigment {White*0.2}}
#declare Line = 0.015;
#declare LinePigment = pigment {Yellow+White/2}
#declare Slice = 0.1;
#declare Sphere = sphere {0, 0.5 }
#declare Box = box {<-1, 0, -1> <1, -Slice, 1>}
#declare E = 0.000001;
#for (M, -0.5, 0.5, Slice)
intersection {
object {Sphere}
object {Box translate y*M}
translate x*M*10
pigment {Red}
}
#end
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