Death Star: Difference between revisions
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=={{header|J}}== |
=={{header|J}}== |
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{{Trans|Python}} |
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<lang J>mag =: +/&.:*:"1 |
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norm=: %"1 0 mag |
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dot =: +/@:*"1 |
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NB. (x,y) getvec pos;posr;neg;negr |
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getvec =: 4 :0 "1 |
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pt =. y |
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'pos posr neg negr' =. x |
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if. (dot~ pt-}:pos) > *:posr do. |
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0 0 0 |
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else. |
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zb =. ({:pos) (+,-) posr -&.:*: pt mag@:- }:pos |
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if. (dot~ pt-}:neg) > *:negr do. |
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(pt,{.zb) - pos |
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else. |
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zs =. ({:neg) (+,-) negr -&.:*: pt mag@:- }:neg |
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if. +./ zs>zb do. |
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if. zs >&{. zb do. 0 0 0 else. (pt,{.zb) - pos end. |
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elseif. ({:zs) < ({.zb) do. neg - (pt,{:zs) |
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elseif. do. (pt,{.zb) - pos end. |
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end. |
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end. |
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) |
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NB. (k;ambient;light) draw_sphere (pos;posr;neg;negr) |
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draw_sphere =: 4 :0 |
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'pos posr neg negr' =. y |
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'k ambient light' =. x |
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shades=. '.:!*oe&#%@' |
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vec=. norm y getvec ,"0// (2{.pos) +/ i: 200 j.~ 0.5+posr |
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b=. (mag vec) * ambient + k * 0>. light dot vec return. |
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intensity=. <. (#shades) * -.b |
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intensity{shades |
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) |
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togray =: 256#. 255 255 255 <.@*"1 0 (%>./@,) |
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env=.(2; 0.5; (norm _50 30 50)) |
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sph=. 20 20 0; 20; 1 1 _6; 20 |
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'rgb' viewmat togray env draw_sphere sph</lang> |
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'''Alternative Solution:''' |
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This version draws planar slices through a sphere. Multiple spheres may be removed. Thus will show holes as well as the exterior. Examples of the defined functions follow the sphere display. |
This version draws planar slices through a sphere. Multiple spheres may be removed. Thus will show holes as well as the exterior. Examples of the defined functions follow the sphere display. |
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Revision as of 19:51, 25 August 2011
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>
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;
/* 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() { normalize(light);
draw_sphere(2, .5); return 0; }</lang>output<lang> eeeee:::::::
eeeeeeeee..............
ooeeeeeeeeee..................
ooooeeeeeeeee......................
oooooooeeeeeeee..........................
ooooooooooeeeee..............................
**ooooooooooeeee.................................
****ooooooooooee.....................................
!*****ooooooooooe.......................................
!!!*****ooooooooo:..........................................
:!!!!*****ooooooo:::...........................................
:::!!!!*****ooooo!:::::...........................................
::::!!!!!*****ooo!!!!::::............................................
.::::!!!!*****oo*!!!!!::::............................................
...::::!!!!*********!!!!:::::............................................
...::::!!!!****o*****!!!!!::::............................................
....::::!!!!***ooo******!!!!!::::............................................
....::::!!!!*ooooooo*****!!!!!:::::...........................................
...::::!!!!!oooooooooo*****!!!!!:::::..........................................
- !!!!eeooooooooooo******!!!!!:::::.........................................
!!!!!eeeeeeeooooooooooo******!!!!!:::::........................................ eeeeeeeeeeeeoooooooooooo******!!!!!:::::....................................... 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, 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. (x,y) getvec pos;posr;neg;negr 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.
if. zs >&{. zb do. 0 0 0 else. (pt,{.zb) - pos end.
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
shades=. '.:!*oe&#%@'
vec=. norm y getvec ,"0// (2{.pos) +/ i: 200 j.~ 0.5+posr
b=. (mag vec) * ambient + k * 0>. light dot vec return.
intensity=. <. (#shades) * -.b
intensity{shades
)
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 draws planar slices through a sphere. Multiple spheres may be removed. Thus will show holes as well as the exterior. Examples of the defined functions follow the sphere display.
<lang J>
coordinates=: %~ ((,"1 0~)"0 3 (,"0)"1 0~)@:i:
length=: +/ &.: *:
centers=: _ 3&{.
radii=: _ _1&{.
]spheres=: 3 1 #"1 ] 0 1,_1 1,:0.3 0.6 NB. spheres x y z r 0 0 0 1 _1 _1 _1 1
0.3 0.3 0.3 0.6
NB. SlicePittedSphere removes the beheaded list of spheres NB. from the head of the list of spheres. NB. It does this over the entire coordinate grid for each NB. sphere (determined by ", the rank conjunction). The NB. boolean arrays are 1 where the length of the vector to NB. the coordinate grid is within the sphere radius.
SlicePittedSphere=: ({. > [: +./ }.)@:((radii@[ >:"0 _1 ] length@:-"1"_ 1 centers@:[) coordinates)~
resolution=: 4
NB. Use the binary array as an index into the literal '@ ' NB. and expand the columns to roughly compensate for the NB. character cell aspect ratio. NB. Boxing matrices (<"2) facilitates display.
<"2]1j1#"1'@ '{~ resolution SlicePittedSphere spheres
┌──────────────────┬──────────────────┬──────────────────┬──────────────────┬──────────────────┬──────────────────┬──────────────────┬──────────────────┬──────────────────┐ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ │@ @ @ @ │@ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ │@ @ @ │@ @ │@ @ │@ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ │@ @ @ │@ @ │@ @ │@ @ @ @ │@ @ @ │@ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ │@ @ @ @ │@ @ │@ @ │ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ │@ @ │@ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ │@ @ @ @ │@ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ │@ @ @ @ │@ @ @ @ @ @ │@ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │@ @ @ @ @ @ @ @ @ │ └──────────────────┴──────────────────┴──────────────────┴──────────────────┴──────────────────┴──────────────────┴──────────────────┴──────────────────┴──────────────────┘
NB. examples of the defined verbs
spheres 0 0 0 1 _1 _1 _1 1
0.3 0.3 0.3 0.6
radii spheres
1 1 0.6
centers spheres 0 0 0 _1 _1 _1
0.3 0.3 0.3
length 3 4 NB. is the sum under squares
5
(,: length&.>) 3 4 ; 2 4 4 ; 5 ? 10
┌───┬─────┬─────────┐ │3 4│2 4 4│3 8 4 9 0│ ├───┼─────┼─────────┤ │5 │6 │13.0384 │ └───┴─────┴─────────┘
NB. coordinates generates a 3D array of x y z triples on [_1:1] NB. by concatenating index vector to itself along various axes. NB. The odometer essay explains several general and simpler sentences. NB. http://www.jsoftware.com/jwiki/Essays/Odometer
i: 2
_2 _1 0 1 2
(%~ i:)2
_1 _0.5 0 0.5 1
NB. box by leading dimension to facilitate display <"_1 coordinates 2x NB. demonstrate with rational numbers
┌────────────┬──────────────┬───────────┬─────────────┬───────────┐ │ _1 _1 _1│ _1 _1 _1r2│ _1 _1 0│ _1 _1 1r2│ _1 _1 1│ │_1r2 _1 _1│_1r2 _1 _1r2│_1r2 _1 0│_1r2 _1 1r2│_1r2 _1 1│ │ 0 _1 _1│ 0 _1 _1r2│ 0 _1 0│ 0 _1 1r2│ 0 _1 1│ │ 1r2 _1 _1│ 1r2 _1 _1r2│ 1r2 _1 0│ 1r2 _1 1r2│ 1r2 _1 1│ │ 1 _1 _1│ 1 _1 _1r2│ 1 _1 0│ 1 _1 1r2│ 1 _1 1│ │ │ │ │ │ │ │ _1 _1r2 _1│ _1 _1r2 _1r2│ _1 _1r2 0│ _1 _1r2 1r2│ _1 _1r2 1│ │_1r2 _1r2 _1│_1r2 _1r2 _1r2│_1r2 _1r2 0│_1r2 _1r2 1r2│_1r2 _1r2 1│ │ 0 _1r2 _1│ 0 _1r2 _1r2│ 0 _1r2 0│ 0 _1r2 1r2│ 0 _1r2 1│ │ 1r2 _1r2 _1│ 1r2 _1r2 _1r2│ 1r2 _1r2 0│ 1r2 _1r2 1r2│ 1r2 _1r2 1│ │ 1 _1r2 _1│ 1 _1r2 _1r2│ 1 _1r2 0│ 1 _1r2 1r2│ 1 _1r2 1│ │ │ │ │ │ │ │ _1 0 _1│ _1 0 _1r2│ _1 0 0│ _1 0 1r2│ _1 0 1│ │_1r2 0 _1│_1r2 0 _1r2│_1r2 0 0│_1r2 0 1r2│_1r2 0 1│ │ 0 0 _1│ 0 0 _1r2│ 0 0 0│ 0 0 1r2│ 0 0 1│ │ 1r2 0 _1│ 1r2 0 _1r2│ 1r2 0 0│ 1r2 0 1r2│ 1r2 0 1│ │ 1 0 _1│ 1 0 _1r2│ 1 0 0│ 1 0 1r2│ 1 0 1│ │ │ │ │ │ │ │ _1 1r2 _1│ _1 1r2 _1r2│ _1 1r2 0│ _1 1r2 1r2│ _1 1r2 1│ │_1r2 1r2 _1│_1r2 1r2 _1r2│_1r2 1r2 0│_1r2 1r2 1r2│_1r2 1r2 1│ │ 0 1r2 _1│ 0 1r2 _1r2│ 0 1r2 0│ 0 1r2 1r2│ 0 1r2 1│ │ 1r2 1r2 _1│ 1r2 1r2 _1r2│ 1r2 1r2 0│ 1r2 1r2 1r2│ 1r2 1r2 1│ │ 1 1r2 _1│ 1 1r2 _1r2│ 1 1r2 0│ 1 1r2 1r2│ 1 1r2 1│ │ │ │ │ │ │ │ _1 1 _1│ _1 1 _1r2│ _1 1 0│ _1 1 1r2│ _1 1 1│ │_1r2 1 _1│_1r2 1 _1r2│_1r2 1 0│_1r2 1 1r2│_1r2 1 1│ │ 0 1 _1│ 0 1 _1r2│ 0 1 0│ 0 1 1r2│ 0 1 1│ │ 1r2 1 _1│ 1r2 1 _1r2│ 1r2 1 0│ 1r2 1 1r2│ 1r2 1 1│ │ 1 1 _1│ 1 1 _1r2│ 1 1 0│ 1 1 1r2│ 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>