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".)
See also: Draw a sphere.
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>
- include <unistd.h>
char shades[] = ".:!*oe&#%@";
double light[3] = { -50, 0, 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;
/* positive shpere and negative sphere */ sphere_t pos = { 20, 20, 0, 20 }, neg = { 1, 1, -6, 20 };
/* 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(pos.cy - pos.r); i <= ceil(pos.cy + pos.r); i++) { y = i + .5; for (j = floor(pos.cx - 2 * pos.r); j <= ceil(pos.cx + 2 * pos.r); j++) { x = (j - pos.cx) / 2. + .5 + pos.cx;
/* ray lands in blank space, draw bg */ if (!hit_sphere(&pos, x, y, &zb1, &zb2)) hit_result = 0;
/* ray hits pos sphere but not neg, draw pos sphere surface */ else if (!hit_sphere(&neg, x, y, &zs1, &zs2)) hit_result = 1;
/* ray hits both, but pos front surface is closer */ else if (zs1 > zb1) hit_result = 1;
/* pos sphere surface is inside neg sphere, show bg */ else if (zs2 > zb2) hit_result = 0;
/* back surface on neg sphere is inside pos sphere, the only place where neg 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 - pos.cx; vec[1] = y - pos.cy; vec[2] = zb1 - pos.cz; break; default: vec[0] = neg.cx - x; vec[1] = neg.cy - y; vec[2] = neg.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() { double ang = 0;
while (1) { printf("\033[H"); light[1] = cos(ang * 2); light[2] = cos(ang); light[0] = sin(ang); normalize(light); ang += .05;
draw_sphere(2, .3); usleep(100000); } return 0; }</lang>
D
<lang d>import std.stdio, std.math, std.numeric, std.algorithm;
/*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&#%@"; // positive and negative spheres enum pos = Sphere(20, 20, 0, 20); enum neg = Sphere(1, 1, -6, 20);
foreach (int i; cast(int)floor(pos.cy - pos.r) ..
cast(int)ceil(pos.cy + pos.r) + 1) {
immutable double y = i + 0.5;
jloop:
foreach (int j; cast(int)floor(pos.cx - 2 * pos.r) ..
cast(int)ceil(pos.cx + 2 * pos.r) + 1) {
immutable double x = (j - pos.cx) / 2.0 + 0.5 + pos.cx;
enum Hit { background, posSphere, negSphere }
Hit hitResult;
double zb1, zs2;
{
double zb2, zs1;
if (!hitSphere(pos, x, y, zb1, zb2)) {
// Ray lands in blank space, draw bg
hitResult = Hit.background;
} else if (!hitSphere(neg, x, y, zs1, zs2)) {
// Ray hits pos sphere but not neg one,
// draw pos sphere surface
hitResult = Hit.posSphere;
} else if (zs1 > zb1) {
// ray hits both, but pos front surface is closer
hitResult = Hit.posSphere;
} else if (zs2 > zb2) {
// pos sphere surface is inside neg sphere,
// show bg
hitResult = Hit.background;
} else if (zs2 > zb1) {
// Back surface on neg sphere is inside pos
// sphere, the only place where neg sphere
// surface will be shown
hitResult = Hit.negSphere;
} else {
hitResult = Hit.posSphere;
}
}
V3 vec_;
final switch (hitResult) {
case Hit.background:
putchar(' ');
continue jloop;
case Hit.posSphere:
vec_ = V3([x - pos.cx, y - pos.cy, zb1 - pos.cz]);
break;
case Hit.negSphere:
vec_ = V3([neg.cx-x, neg.cy-y, neg.cz-zs2]);
break;
}
immutable V3 nvec = vec_.normalize;
immutable double b = light.dot(nvec) ^^ k + ambient;
int intensity = cast(int)((1 - b) * shades.length);
intensity = min(shades.length, max(0, intensity));
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>
J
<lang J>mag =: +/&.:*:"1 norm=: %"1 0 mag dot =: +/@:*"1
NB. (pos;posr;neg;negr) getvec (x,y) getvec =: 4 :0 "1
pt =. y
'pos posr neg negr' =. x
if. (dot~ pt-}:pos) > *:posr do.
0 0 0
else.
zb =. ({:pos) (-,+) posr -&.:*: pt mag@:- }:pos
if. (dot~ pt-}:neg) > *:negr do.
(pt,{:zb) - pos
else.
zs =. ({:neg) (-,+) negr -&.:*: pt mag@:- }:neg
if. zs >&{. zb do. (pt,{:zb) - pos
elseif. zs >&{: zb do. 0 0 0
elseif. ({.zs) < ({:zb) do. neg - (pt,{.zs)
elseif. do. (pt,{.zb) - pos end.
end.
end.
)
NB. (k;ambient;light) draw_sphere (pos;posr;neg;negr)
draw_sphere =: 4 :0
'pos posr neg negr' =. y
'k ambient light' =. x
vec=. norm y getvec ,"0// (2{.pos) +/ i: 200 j.~ 0.5+posr
b=. (mag vec) * ambient + k * 0>. light dot vec
)
togray =: 256#. 255 255 255 <.@*"1 0 (%>./@,)
env=.(2; 0.5; (norm _50 30 50)) sph=. 20 20 0; 20; 1 1 _6; 20 'rgb' viewmat togray env draw_sphere sph</lang>
Alternative Solution:
This version classifies surface normals by comparison to reference surfaces. Multiple spheres may be removed. Exercises for the intrepid student: enhance color resolution with more reference surfaces or combinations of all surfaces matching better than some criterion, incorporate ThinFaces for anti-aliasing, map the colors for realism.
<lang J> load'graphics/viewmat'
resolution=: 8 spheres=: 3 1 #"1 ] 0 1,_1 1,:0.3 0.6 NB. spheres x y z r
coordinates=: (% <:)~ (,"1 0~"0 3 ,"0"1 0~)@:i:
length=: +/ &.: *:
centers=: _ 3&{.
radii=: _ _1&{.
NB. resolution SlicePittedSphere spheres generates a binary array, 1 in the geometric object SlicePittedSphere=: (0 { {. > [: +./ }.)@:(radii@[ >:"0 3 ((length@:-"1"_ 1 centers)~ coordinates))~
spanTo=: conjunction def '(m<:y)*.y<:n' NB. algebraic similarity, m <= y <= n
tessellate=: ] ];._3"3~ 3 # [ NB. All cubical edge length x subarrays of array y
NB. Define "faces" as those points with 9 to 18 inclusive "solid" neighbors. detectFace=: (9 spanTo 18) @: (+/@:,"3) @: (3&tessellate)
NB. arrange faces in ANSYS brick face order ThickFaces=: ((|:"3 , (, |:"2))(,: |."1)3 3 3$2j1#1) /: 'SENWDU' i. 'DUEWSN' ThinFaces=: ((|:"3 , (, |:"2))(,: |."1)3 3 3$1j2#1) /: 'SENWDU' i. 'DUEWSN'
FACES=:ThickFaces NB. 6 below comes from #Faces
NORMALS=: 2 tessellate FACES
matchNormals=: [: +/@,"6 NORMALS ="6"6 _ (2 tessellate 3 tessellate ])
bestFit=: (i.>./)"1&.|:
topFace=: detectFace i:"1 1:
choose=: 4 : 'x}y'
viewmat resolution (topFace choose (,&(#FACES))@:bestFit@matchNormals)@SlicePittedSphere spheres
<"_1 ThickFaces NB. display the 6 cubes with reference faces
┌─────┬─────┬─────┬─────┬─────┬─────┐ │1 1 1│1 1 0│0 0 0│0 1 1│1 1 1│0 0 0│ │1 1 1│1 1 0│1 1 1│0 1 1│1 1 1│0 0 0│ │0 0 0│1 1 0│1 1 1│0 1 1│1 1 1│0 0 0│ │ │ │ │ │ │ │ │1 1 1│1 1 0│0 0 0│0 1 1│1 1 1│1 1 1│ │1 1 1│1 1 0│1 1 1│0 1 1│1 1 1│1 1 1│ │0 0 0│1 1 0│1 1 1│0 1 1│1 1 1│1 1 1│ │ │ │ │ │ │ │ │1 1 1│1 1 0│0 0 0│0 1 1│0 0 0│1 1 1│ │1 1 1│1 1 0│1 1 1│0 1 1│0 0 0│1 1 1│ │0 0 0│1 1 0│1 1 1│0 1 1│0 0 0│1 1 1│ └─────┴─────┴─────┴─────┴─────┴─────┘ </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 $pos = [ 120, 120, 0, 120 ]; my $neg = [ -77, -33, -100, 190 ]; my $light = normalize([ -12, 13, -10 ]); sub draw { my ($k, $amb) = @_; binmode STDOUT, ":raw"; print "P5\n", $pos->[0] * 2 + 3, " ", $pos->[1] * 2 + 3, "\n255\n"; for my $y (($pos->[1] - $pos->[3] - 1) .. ($pos->[1] + $pos->[3] + 1)) { my @row = (); for my $x (($pos->[0] - $pos->[3] - 1) .. ($pos->[0] + $pos->[3] + 1)) { my ($hit, @hs) = 0; my @h = hit($pos, $x, $y);
if (!@h) { $hit = 0 } elsif (!(@hs = hit($neg, $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 - $pos->[0], $y - $pos->[1], $h[0] - $pos->[2] ]; } else { $v = [ $neg->[0] - $x, $neg->[1] - $y, $neg->[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(2, 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([ 4, -1, -3 ]);
- positive sphere at origin
my $pos = sphere.new(
cx => 0, cy => 0, cz => 0, r => $s.Int
);
- negative sphere offset to upper left
my $neg = sphere.new(
cx => (-$s*.90).Int, cy => (-$s*.90).Int, cz => (-$s*.3).Int, r => ($s*.7).Int
);
sub MAIN ($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 $bs = "\b" x 8;
for ($pos.cy - $pos.r) .. ($pos.cy + $pos.r) -> $y {
note $bs, $y, ' '; # monitor progress
for ($pos.cx - $pos.r) .. ($pos.cx + $pos.r) -> $x {
# black if we don't hit positive sphere, ignore negative sphere
if not hit($pos, $x, $y, my $posz) {
@pixels.push(0);
next;
}
my @vec;
# is front of positive sphere inside negative sphere?
if hit($neg, $x, $y, my $negz) and $negz.min < $posz.min < $negz.max {
# make black if whole positive sphere eaten here
if $negz.min < $posz.max < $negz.max { @pixels.push(0); next; }
# render inside of negative sphere
@vec = normalize([$neg.cx - $x, $neg.cy - $y, -$negz.max - $neg.cz]);
}
else {
# render outside of positive sphere
@vec = normalize([$x - $pos.cx, $y - $pos.cy, $posz.max - $pos.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>
Python
<lang python>import sys, math, collections
Sphere = collections.namedtuple("Sphere", "cx cy cz r") V3 = collections.namedtuple("V3", "x y z")
def normalize((x, y, z)):
len = math.sqrt(x**2 + y**2 + z**2) return V3(x / len, y / len, z / len)
def dot(v1, v2):
d = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z return -d if d < 0 else 0.0
def hit_sphere(sph, x0, y0):
x = x0 - sph.cx
y = y0 - sph.cy
zsq = sph.r ** 2 - (x ** 2 + y ** 2)
if zsq < 0:
return (False, 0, 0)
szsq = math.sqrt(zsq)
return (True, sph.cz - szsq, sph.cz + szsq)
def draw_sphere(k, ambient, light):
shades = ".:!*oe&#%@" pos = Sphere(20.0, 20.0, 0.0, 20.0) neg = Sphere(1.0, 1.0, -6.0, 20.0)
for i in xrange(int(math.floor(pos.cy - pos.r)),
int(math.ceil(pos.cy + pos.r) + 1)):
y = i + 0.5
for j in xrange(int(math.floor(pos.cx - 2 * pos.r)),
int(math.ceil(pos.cx + 2 * pos.r) + 1)):
x = (j - pos.cx) / 2.0 + 0.5 + pos.cx
(h, zb1, zb2) = hit_sphere(pos, x, y)
if not h:
hit_result = 0
else:
(h, zs1, zs2) = hit_sphere(neg, x, y)
if not h:
hit_result = 1
elif zs1 > zb1:
hit_result = 1
elif zs2 > zb2:
hit_result = 0
elif zs2 > zb1:
hit_result = 2
else:
hit_result = 1
if hit_result == 0:
sys.stdout.write(' ')
continue
elif hit_result == 1:
vec = V3(x - pos.cx, y - pos.cy, zb1 - pos.cz)
elif hit_result == 2:
vec = V3(neg.cx-x, neg.cy-y, neg.cz-zs2)
vec = normalize(vec)
b = dot(light, vec) ** k + ambient
intensity = int((1 - b) * len(shades))
intensity = min(len(shades), max(0, intensity))
sys.stdout.write(shades[intensity])
print
light = normalize(V3(-50, 30, 50)) draw_sphere(2, 0.5, light)</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>
Tcl
Note that this code has a significant amount of refactoring relative to the C version, including the addition of specular reflections and the separation of the scene code from the raytracing from the rendering. <lang tcl>package require Tcl 8.5
proc normalize vec {
upvar 1 $vec v
lassign $v x y z
set len [expr {sqrt($x**2 + $y**2 + $z**2)}]
set v [list [expr {$x/$len}] [expr {$y/$len}] [expr {$z/$len}]]
return
}
proc dot {a b} {
lassign $a ax ay az
lassign $b bx by bz
return [expr {-($ax*$bx + $ay*$by + $az*$bz)}]
}
- Intersection code; assumes that the vector is parallel to the Z-axis
proc hitSphere {sphere x y z1 z2} {
dict with sphere {
set x [expr {$x - $cx}] set y [expr {$y - $cy}] set zsq [expr {$r**2 - $x**2 - $y**2}] if {$zsq < 0} {return 0} upvar 1 $z1 _1 $z2 _2 set zsq [expr {sqrt($zsq)}] set _1 [expr {$cz - $zsq}] set _2 [expr {$cz + $zsq}] return 1
}
}
- How to do the intersection with our scene
proc intersectDeathStar {x y vecName} {
global big small
if {![hitSphere $big $x $y zb1 zb2]} {
# ray lands in blank space return 0
}
upvar 1 $vecName vec
# ray hits big sphere; check if it hit the small one first
set vec [if {
![hitSphere $small $x $y zs1 zs2] || $zs1 > $zb1 || $zs2 <= $zb1
} then {
dict with big { list [expr {$x - $cx}] [expr {$y - $cy}] [expr {$zb1 - $cz}] }
} else {
dict with small { list [expr {$cx - $x}] [expr {$cy - $y}] [expr {$cz - $zs2}] }
}] normalize vec return 1
}
- Intensity calculators for different lighting components
proc diffuse {k intensity L N} {
expr {[dot $L $N] ** $k * $intensity}
} proc specular {k intensity L N S} {
# Calculate reflection vector
set r [expr {2 * [dot $L $N]}]
foreach l $L n $N {lappend R [expr {$l-$r*$n}]}
normalize R
# Calculate the specular reflection term
return [expr {[dot $R $S] ** $k * $intensity}]
}
- Simple raytracing engine that uses parallel rays
proc raytraceEngine {diffparms specparms ambient intersector shades renderer fx tx sx fy ty sy} {
global light
for {set y $fy} {$y <= $ty} {set y [expr {$y + $sy}]} {
set line {} for {set x $fx} {$x <= $tx} {set x [expr {$x + $sx}]} { if {![$intersector $x $y vec]} { # ray lands in blank space set intensity end } else { # ray hits something; we've got the normalized vector set b [expr { [diffuse {*}$diffparms $light $vec] + [specular {*}$specparms $light $vec {0 0 -1}] + $ambient }] set intensity [expr {int((1-$b) * ([llength $shades]-1))}] if {$intensity < 0} { set intensity 0 } elseif {$intensity >= [llength $shades]-1} { set intensity end-1 } } lappend line [lindex $shades $intensity] } {*}$renderer $line
}
}
- The general scene settings
set light {-50 30 50} set big {cx 20 cy 20 cz 0 r 20} set small {cx 7 cy 7 cz -10 r 15} normalize light
- Render as text
proc textDeathStar {diff spec lightBrightness ambient} {
global big
dict with big {
raytraceEngine [list $diff $lightBrightness] \ [list $spec $lightBrightness] $ambient intersectDeathStar \ [split ".:!*oe&#%@ " {}] {apply {l {puts [join $l ""]}}} \ [expr {$cx+floor(-$r)}] [expr {$cx+ceil($r)+0.5}] 0.5 \ [expr {$cy+floor(-$r)+0.5}] [expr {$cy+ceil($r)+0.5}] 1
}
} textDeathStar 3 10 0.7 0.3</lang> Output:
#######&eeeeeeeee
ee&&&&&&########%eeoooooooooooe
**oooee&&&&&&########%ooooo**********oo
!!!***oooee&&&&&&########%********!!!!!!!!***
!!!!!!!****ooee&&&&&&#######%*****!!!!!!!!!!!!!!!**
::::!!!!!!***oooee&&&&&&######***!!!!!!!::::::::::::!!*
:::::::!!!!!!***ooeee&&&&&&#####**!!!!!!:::::::::::::::::!*
::::::::::!!!!!***oooee&&&&&&####*!!!!!!::::::::.........::::!*
::::::::::!!!!!!***oooeee&&&&&&###!!!!!!:::::::..............:::!
..:::::::::!!!!!!****oooeee&&&&&&##!!!!!!::::::..................::!*
...::::::::!!!!!!****ooooeee&&&&&&!!!!!!:::::::....................::!*
....::::::!!!!!!*****ooooeeee&&&&&!!!!!!:::::::......................::!*
....::::::!!!!!*****oooooeeeee&&&&!!!!!!::::::::.......................::!*
...::::::!!!!!*****oooooeeeee&&&!!!!!!:::::::::.........................::!
...:::::!!!!!*****oooooeeeeee&&!!!!!!!:::::::::..........................::!*
..:::::!!!!!****oooooeeeeee&&&!!!!!!!::::::::::..........................::!!
.::::::!!!!*****ooooeeeeee&&*!!!!!!!::::::::::::.........................:::!!*
:::::!!!!!****oooooeeeee&&**!!!!!!!::::::::::::::.......................::::!!*
!!!!!!!!****oooooeeeee&****!!!!!!!::::::::::::::::::..................::::::!!*
#!!!******oooooeeeeeoo*****!!!!!!!:::::::::::::::::::::::::::::::::::::::::!!!*
##oooooooooooeeeeeeoooo****!!!!!!!:::::::::::::::::::::::::::::::::::::::!!!!**
%#####eeee&&&&&&&eeeooo****!!!!!!!!:::::::::::::::::::::::::::::::::::!!!!!!**o
%#########&&&&&&&&eeeooo****!!!!!!!!!::::::::::::::::::!!!!!!!!!!!!!!!!!!!****o
%##########&&&&&&&&eeeooo****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!****ooe
%##########&&&&&&&&eeeooo*****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!**********ooo
%%##########&&&&&&&&eeeoooo*****!!!!!!!!!!!!!!!!!!!*********************ooooe
%%##########&&&&&&&&eeeoooo***************************************oooooooee
@%###########&&&&&&&&&eeeooooo*************************ooooooooooooooooeee&
@%###########&&&&&&&&&eeeeoooooo*************ooooooooooooooooooooooeeeee&
@%%##########&&&&&&&&&&eeeeoooooooooooooooooooooooooooooooeeeeeeeeeee&&
@%%###########&&&&&&&&&&eeeeeoooooooooooooooooooeeeeeeeeeeeeeeeeee&&&
%%############&&&&&&&&&&eeeeeeeeeeooeeeeeeeeeeeeeeeeeeeeeeee&&&&&
@%%###########&&&&&&&&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&&
%%############&&&&&&&&&&&&&&eeeeeeeeeeeeeee&&&&&&&&&&&&&&&&
%%############&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
%%#############&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
%%#############&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
%##############&&&&&&&&&&&&&&&&&&&&&&&&
%##############&&&&&&&&&&&&&&&&
#################
To render it as an image, we just supply different code to map the intensities to displayable values:
<lang tcl># Render as a picture (with many hard-coded settings) package require Tk proc guiDeathStar {photo diff spec lightBrightness ambient} {
set row 0
for {set i 255} {$i>=0} {incr i -1} {
lappend shades [format "#%02x%02x%02x" $i $i $i]
} raytraceEngine [list $diff $lightBrightness] \
[list $spec $lightBrightness] $ambient intersectDeathStar \ $shades {apply {l { upvar 2 photo photo row row $photo put [list $l] -to 0 $row incr row update }}} 0 40 0.0625 0 40 0.0625 } pack [label .l -image [image create photo ds]] guiDeathStar ds 3 10 0.7 0.3</lang>