Death Star
You are encouraged to solve this task according to the task description, using any language you may know.
Death Star is a task to display a region that consists of a large sphere with part of a smaller sphere removed from it as a result of geometric subtraction. (This will basically produce a shape like a "death star".)
Brlcad
<lang brlcad># We need a database to hold the objects opendb deathstar.g y
- We will be measuring in kilometers
units km
- Create a sphere of radius 60km centred at the origin
in sph1.s sph 0 0 0 60
- We will be subtracting an overlapping sphere with a radius of 40km
- The resultant hole will be smaller than this, because we only
- only catch the edge
in sph2.s sph 0 90 0 40
- Create a region named deathstar.r which consists of big minus small sphere
r deathstar.r u sph1.s - sph2.s
- We will use a plastic material texture with rgb colour 224,224,224
- with specular lighting value of 0.1 and no inheritance
mater deathstar.r "plastic sp=0.1" 224 224 224 0
- Clear the wireframe display and draw the deathstar
B deathstar.r
- We now trigger the raytracer to see our finished product
rt</lang>
C
Primitive ray tracing. <lang c>#include <stdio.h>
- include <math.h>
char shades[] = ".:!*oe&#%@";
double light[3] = { -50, 30, 50 }; void normalize(double * v) { double len = sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= len; v[1] /= len; v[2] /= len; }
double dot(double *x, double *y) { double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2]; return d < 0 ? -d : 0; }
typedef struct { double cx, cy, cz, r; } sphere_t; sphere_t big = { 20, 20, 0, 20 }, small = { 7, 7, -10, 15 };
/* check if a ray (x,y, -inf)->(x, y, inf) hits a sphere; if so, return
the intersecting z values. z1 is closer to the eye */
int hit_sphere(sphere_t *sph, double x, double y, double *z1, double *z2) { double zsq; x -= sph->cx; y -= sph->cy; zsq = sph->r * sph->r - (x * x + y * y); if (zsq < 0) return 0; zsq = sqrt(zsq); *z1 = sph->cz - zsq; *z2 = sph->cz + zsq; return 1; }
void draw_sphere(double k, double ambient) { int i, j, intensity, hit_result; double b; double vec[3], x, y, zb1, zb2, zs1, zs2; for (i = floor(big.cy - big.r); i <= ceil(big.cy + big.r); i++) { y = i + .5; for (j = floor(big.cx - 2 * big.r); j <= ceil(big.cx + 2 * big.r); j++) { x = (j - big.cx) / 2. + .5 + big.cx;
/* ray lands in blank space, draw bg */ if (!hit_sphere(&big, x, y, &zb1, &zb2)) hit_result = 0;
/* ray hits big sphere but not small one, draw big sphere surface */ else if (!hit_sphere(&small, x, y, &zs1, &zs2)) hit_result = 1;
/* ray hits both, but small surface is obscured by big */ else if (zs1 > zb1) hit_result = 1;
/* both large points entirely inside small sphere, show bg */
else if (zs2 > zb2) hit_result = 0;
/* if deeper intersection on small sphere is inside big sphere, only place where small sphere surface will be shown */ else if (zs2 > zb1) hit_result = 2; else hit_result = 1;
switch(hit_result) { case 0: putchar(' '); continue; case 1: vec[0] = x - big.cx; vec[1] = y - big.cy; vec[2] = zb1 - big.cz; break; default: vec[0] = small.cx - x; vec[1] = small.cy - y; vec[2] = small.cz - zs2; }
normalize(vec); b = pow(dot(light, vec), k) + ambient; intensity = (1 - b) * (sizeof(shades) - 1); if (intensity < 0) intensity = 0; if (intensity >= sizeof(shades) - 1) intensity = sizeof(shades) - 2; putchar(shades[intensity]); } putchar('\n'); } }
int main() { normalize(light);
draw_sphere(2, .5); return 0; }</lang>output<lang> eeeeeee!!!:::::::
ooooooeeeeeeeeeee..............
*ooooooooooeeeeeeeeeee.................
!****ooooooooooeeeeeeeeeee...................
:!!!!*****oooooooooeeeeeeeeee......................
::::!!!!*****oooooooooeeeeeeee.........................
....:::!!!!*****ooooooooeeeeeeee...........................
.......:::!!!!*****ooooooooeeeeee..............................
.........:::!!!!****ooooooooeeeeee...............................
............:::!!!!****ooooooooeeee..................................
.............::::!!!****ooooooooee.....................................
...............:::!!!!****oooooooe.......................................
................::::!!!****ooooooo.........................................
.................:::!!!****ooooo...........................................
..................:::!!!****ooo::............................................
..................:::!!!****oo:::............................................
..................:::!!!!***!!!::::............................................ ..................:::!!!**!!!!!:::::........................................... .................:::!!!****!!!!!:::::.......................................... e...............:::!oo******!!!!!:::::......................................... ee............:::oooooo******!!!!!:::::........................................ eeeeee::::eeoooooooooooo******!!!!!:::::....................................... eeeeeeeeeeeeeoooooooooooo******!!!!!!:::::..................................... eeeeeeeeeeeeeeoooooooooooo******!!!!!!:::::....................................
eeeeeeeeeeeeeeoooooooooooo*******!!!!!!:::::.................................
eeeeeeeeeeeeeeeooooooooooooo******!!!!!!::::::..............................:
eeeeeeeeeeeeeeeooooooooooooo*******!!!!!!:::::::..........................:
eeeeeeeeeeeeeeeeoooooooooooooo*******!!!!!!!:::::::.....................::!
eeeeeeeeeeeeeeeeeooooooooooooo********!!!!!!!:::::::::..............::::!
eeeeeeeeeeeeeeeeeoooooooooooooo********!!!!!!!!::::::::::::::::::::::!*
eeeeeeeeeeeeeeeeeeooooooooooooooo********!!!!!!!!!!:::::::::::::!!!!*
eeeeeeeeeeeeeeeeeoooooooooooooooo**********!!!!!!!!!!!!!!!!!!!!!*
eeeeeeeeeeeeeeeeeeooooooooooooooooo************!!!!!!!!!!!!****
eeeeeeeeeeeeeeeeeeoooooooooooooooooo**********************o
eeeeeeeeeeeeeeeeeeeooooooooooooooooooooo************ooo
eeeeeeeeeeeeeeeeeeeeooooooooooooooooooooooooooooooo
eeeeeeeeeeeeeeeeeeeeooooooooooooooooooooooooo
eeeeeeeeeeeeeeeeeeeeeoooooooooooooooooo
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeee</lang>
D
<lang d>import std.stdio, std.math, std.numeric;
/*const*/ struct V3 {
double[3] v;
@property V3 normalize() pure nothrow const {
//immutable double len = sqrt(dotProduct(v, v));
immutable double len= sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
// return V3(v[] / len);
return V3([v[0] / len, v[1] / len, v[2] / len]);
}
double dot(const ref V3 y) pure nothrow const {
immutable double d = dotProduct(v, y.v);
return d < 0 ? -d : 0;
}
}
const struct Sphere { double cx, cy, cz, r; }
void drawSphere(in double k, in double ambient, in V3 light)nothrow{
/** Check if a ray (x,y, -inf).(x, y, inf) hits a sphere; if so,
return the intersecting z values. z1 is closer to the eye */
static bool hitSphere(const ref Sphere sph,
in double x0, in double y0,
out double z1,
out double z2) pure nothrow {
immutable double x = x0 - sph.cx;
immutable double y = y0 - sph.cy;
immutable double zsq = sph.r ^^ 2 - (x ^^ 2 + y ^^ 2);
if (zsq < 0)
return false;
immutable double szsq = sqrt(zsq);
z1 = sph.cz - szsq;
z2 = sph.cz + szsq;
return true;
}
enum string shades = ".:!*oe&#%@"; enum big = Sphere(20, 20, 0, 20); enum small = Sphere(7, 7, -10, 15);
foreach (int i; cast(int)floor(big.cy - big.r) ..
cast(int)ceil(big.cy + big.r) + 1) {
immutable double y = i + 0.5;
jloop:
foreach (int j; cast(int)floor(big.cx - 2 * big.r) ..
cast(int)ceil(big.cx + 2 * big.r) + 1) {
immutable double x = (j - big.cx) / 2.0 + 0.5 + big.cx;
enum Hit { background, bigSphere, smallSphere }
Hit hitResult;
double zb1, zs2;
{
double zb2, zs1;
if (!hitSphere(big, x, y, zb1, zb2))
// ray lands in blank space, draw bg
hitResult = Hit.background;
else if (!hitSphere(small, x, y, zs1, zs2))
// ray hits big sphere but not small one,
// draw big sphere surface
hitResult = Hit.bigSphere;
else if (zs1 > zb1)
// ray hits both, but small surface is
// obscured by big
hitResult = Hit.bigSphere;
else if (zs2 > zb2) {
// both large points entirely inside
// small sphere, show bg
hitResult = Hit.background;
}
else if (zs2 > zb1)
// if deeper intersection on small sphere is
// inside big sphere, only place where small
// sphere surface will be shown
hitResult = Hit.smallSphere;
else
hitResult = Hit.bigSphere;
}
V3 vec_;
final switch (hitResult) {
case Hit.background:
putchar(' ');
continue jloop;
case Hit.bigSphere:
vec_ = V3([x - big.cx, y - big.cy, zb1 - big.cz]);
break;
case Hit.smallSphere:
vec_ = V3([small.cx-x, small.cy-y, small.cz-zs2]);
break;
}
immutable V3 nvec = vec_.normalize;
immutable double b = light.dot(nvec) ^^ k + ambient;
immutable intensity = cast(int)((1 - b) * shades.length);
if (intensity < 0)
putchar(shades[0]);
else if (intensity >= shades.length)
putchar(shades[$ - 1]);
else
putchar(shades[intensity]);
}
putchar('\n');
}
}
void main() {
enum light = V3([-50, 30, 50]).normalize; drawSphere(2, 0.5, light);
}</lang> The output is the same of the C version.
DWScript
<lang delphi>const cShades = '.:!*oe&#%@';
type TVector = array [0..2] of Float;
var light : TVector = [-50.0, 30, 50];
procedure Normalize(var v : TVector); begin
var len := Sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= len; v[1] /= len; v[2] /= len;
end;
function Dot(x, y : TVector) : Float; begin
var d :=x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
if d<0 then
Result:=-d
else Result:=0;
end;
type
TSphere = record
cx, cy, cz, r : Float;
end;
const big : TSphere = (cx: 20; cy: 20; cz: 0; r: 20); const small : TSphere = (cx: 7; cy: 7; cz: -10; r: 15);
function HitSphere(sph : TSphere; x, y : Float; var z1, z2 : Float) : Boolean; begin
x -= sph.cx; y -= sph.cy; var zsq = sph.r * sph.r - (x * x + y * y); if (zsq < 0) then Exit False; zsq := Sqrt(zsq); z1 := sph.cz - zsq; z2 := sph.cz + zsq; Result:=True;
end;
procedure DrawSphere(k, ambient : Float); var
i, j, intensity : Integer; b : Float; x, y, zb1, zb2, zs1, zs2 : Float; vec : TVector;
begin
for i:=Trunc(big.cy-big.r) to Trunc(big.cy+big.r)+1 do begin
y := i + 0.5;
for j := Trunc(big.cx-2*big.r) to Trunc(big.cx+2*big.r) do begin
x := (j-big.cx)/2 + 0.5 + big.cx;
if not HitSphere(big, x, y, zb1, zb2) then begin
Print(' ');
continue;
end;
if not HitSphere(small, x, y, zs1, zs2) then begin
vec[0] := x - big.cx;
vec[1] := y - big.cy;
vec[2] := zb1 - big.cz;
end else begin
if zs1 < zb1 then begin
if zs2 > zb2 then begin
Print(' ');
continue;
end;
if zs2 > zb1 then begin
vec[0] := small.cx - x;
vec[1] := small.cy - y;
vec[2] := small.cz - zs2;
end else begin
vec[0] := x - big.cx;
vec[1] := y - big.cy;
vec[2] := zb1 - big.cz;
end;
end else begin
vec[0] := x - big.cx;
vec[1] := y - big.cy;
vec[2] := zb1 - big.cz;
end;
end;
Normalize(vec);
b := Power(Dot(light, vec), k) + ambient;
intensity := Round((1 - b) * Length(cShades));
Print(cShades[ClampInt(intensity+1, 1, Length(cShades))]);
end;
PrintLn();
end;
end;
Normalize(light);
DrawSphere(2, 0.3);</lang>
Perl
Writes a PGM to stdout. <lang perl>use strict;
sub sq { my $s = 0; $s += $_ ** 2 for @_; $s; }
sub hit { my ($sph, $x, $y) = @_; $x -= $sph->[0]; $y -= $sph->[1];
my $z = sq($sph->[3]) - sq($x, $y); return if $z < 0;
$z = sqrt $z; return $sph->[2] - $z, $sph->[2] + $z; }
sub normalize { my $v = shift; my $n = sqrt sq(@$v); $_ /= $n for @$v; $v; }
sub dot { my ($x, $y) = @_; my $s = $x->[0] * $y->[0] + $x->[1] * $y->[1] + $x->[2] * $y->[2]; $s > 0 ? $s : 0; }
my $big = [ 120, 120, 0, 120 ]; my $sm = [ 27, 67, -90, 80 ]; my $light = normalize([ 120, -130, -150 ]); sub draw { my ($k, $amb) = @_; binmode STDOUT, ":raw"; print "P5\n", $big->[0] * 2 + 3, " ", $big->[1] * 2 + 3, "\n255\n"; for my $y (($big->[1] - $big->[3] - 1) .. ($big->[1] + $big->[3] + 1)) { my @row = (); for my $x (($big->[0] - $big->[3] - 1) .. ($big->[0] + $big->[3] + 1)) { my ($hit, @hs) = 0; my @h = hit($big, $x, $y);
if (!@h) { $hit = 0 } elsif (!(@hs = hit($sm, $x, $y))) { $hit = 1 } elsif ($hs[0] > $h[0]) { $hit = 1 } elsif ($hs[1] > $h[0]) { $hit = $hs[1] > $h[1] ? 0 : 2 } else { $hit = 1 }
my ($val, $v); if ($hit == 0) { $val = 0 } elsif ($hit == 1) { $v = [ $x - $big->[0], $y - $big->[1], $h[0] - $big->[2] ]; } else { $v = [ $sm->[0] - $x, $sm->[1] - $y, $sm->[2] - $hs[1] ]; } if ($v) { normalize($v); $val = int((dot($v, $light) ** $k + $amb) * 255); $val = ($val > 255) ? 255 : ($val < 0) ? 0 : $val; } push @row, $val; } print pack("C*", @row); } }
draw(4, 0.2);</lang>
Perl 6
Reimplemented to output a .pgm image.
<lang perl6>class sphere {
has $.cx; # center x coordinate has $.cy; # center y coordinate has $.cz; # center z coordinate has $.r; # radius
}
my $depth = 255; # image color depth
my $x = my $y = 255; # dimensions of generated .pgm; must be odd
my $s = ($x - 1)/2; # scaled dimension to build geometry
my @light = normalize([ -2, 4, -5 ]);
- large sphere at origin
my $lg = sphere.new(
cx => 0, cy => 0, cz => 0, r => $s.Int
);
- small sphere offset to upper left
my $sm = sphere.new(
cx => (-$s*.65).Int, cy => (-$s*.65).Int, cz => (-$s*.5).Int, r => ($s*.5).Int
);
sub MAIN ($outfile = 'deathstar-perl6.pgm') {
my $out = open( $outfile, :w, :bin ) or die "$!\n";
$out.say("P5\n$x $y\n$depth"); # .pgm header
say 'Calculating row:';
$out.print( draw_ds(3, .15)».chrs );
$out.close;
}
sub draw_ds ( $k, $ambient ) {
my @pixels;
my $bs = 8.chr x 8;
for ($lg.cy - $lg.r) .. ($lg.cy + $lg.r) -> $y {
print $bs, $y, ' '; # monitor progress
for ($lg.cx - $lg.r) .. ($lg.cx + $lg.r) -> $x {
# black if we don't hit large sphere, ignore small sphere
if not hit($lg, $x, $y, my $lgz) {
@pixels.push(0);
next; }
my @vec;
# is front of large sphere inside small sphere?
if hit($sm, $x, $y, my $smz) and $smz.min < $lgz.min < $smz.max {
# make black if whole large sphere eaten here
if $smz.min < $lgz.max < $smz.max { @pixels.push(0); next; }
# render inside of small sphere
@vec = normalize([$sm.cx - $x, $sm.cy - $y, -$smz.max - $sm.cz]);
}
else { # render outside of large sphere @vec = normalize([$x - $lg.cx, $y - $lg.cy, $lgz.max - $lg.cz]); }
my $intensity = dot(@light, @vec) ** $k + $ambient;
@pixels.push( ($intensity * $depth).Int min $depth );
}
}
say $bs, 'Writing file.';
return @pixels;
}
- normalize a vector
sub normalize (@vec) { return @vec »/» ([+] @vec Z* @vec).sqrt }
- dot product of two vectors
sub dot (@x, @y) { return -([+] @x Z* @y) max 0 }
- are the coordinates within the radius of the sphere?
sub hit ($sphere, $x is copy, $y is copy, $z is rw) {
$x -= $sphere.cx; $y -= $sphere.cy; my $z2 = $sphere.r * $sphere.r - $x * $x - $y * $y; return 0 if $z2 < 0; $z2 = $z2.sqrt; $z = $sphere.cz - $z2 .. $sphere.cz + $z2; return 1;
}</lang>
Openscad
<lang openscad>// We are performing geometric subtraction
difference() {
// Create the primary sphere of radius 60 centred at the origin
translate(v = [0,0,0]) {
sphere(60);
}
/*Subtract an overlapping sphere with a radius of 40
The resultant hole will be smaller than this, because we only
only catch the edge
*/
translate(v = [0,90,0]) {
sphere(40);
}
}</lang>
POV-Ray
<lang POV-Ray>camera { perspective location <0.0 , .8 ,-3.0> look_at 0
aperture .1 blur_samples 20 variance 1/100000 focal_point 0}
light_source{< 3,3,-3> color rgb 1}
sky_sphere { pigment{ color rgb <0,.2,.5>}}
plane {y,-5 pigment {color rgb .54} normal {hexagon} }
difference {
sphere { 0,1 }
sphere { <-1,1,-1>,1 }
texture {
pigment{ granite }
finish { phong 1 reflection {0.10 metallic 0.5} }
}
} </lang>
