Slingshot Home: Escape Saturn

Tharikaa Ramesh Kumar
/
Slingshot Home: Escape Saturn
on 10 Nov 2026
7
65
19
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9998
game.m
function g=game()
%GAME Slingshot Home: a one-button journey from Saturn's moons to Earth.
% Created by Tharikaa Ramesh Kumar.
%
% Tap to launch, then time each tangential boost to reach the next gate.
% Clear 15 moon stages and the escape gate before time or shields run out.
% Gravity bends flights, but the orbits and captures are arcade assists;
% this is a physics-inspired game, not a real mission or ephemeris model.
%
% The contest harness owns input, timing, and drawing. init creates graphics,
% update advances the state, and render displays that state without changing it.
% Comments explain the compact code and are excluded from the contest count.
%
% Modes m: 1 ready, 2 intro, 3 orbit, 4 flight, 5 settling, 6 reserved,
% 7 homecoming, 8 won, 9 over. n=moon, p=position, a=orbit anchor angle.
% c=body centers, d=unit heading, f=flight samples/result, t=game time.
% hp=shields, t0=mode start, v=camera viewport, o=escape point, u=ending time.
g=struct('init',@init,'update',@tick,'render',@draw);
end

function s=init(ax)
% Pool every object. Planets are generated RGB images, with no file access.
% Names are real Saturn moons; placements and sizes are authored game geometry.
ax.XLim=[0 800]; ax.YLim=[0 600]; ax.YDir='normal';
ax.Color='#090b0f'; ax.DataAspectRatio=[1 1 1];
s.names=split("Pan Daphnis Atlas Prometheus Pandora Epimetheus Janus Mimas Enceladus Tethys Dione Rhea Titan Iapetus Phoebe Earth");
a=linspace(0,2*pi,65)'; s.arc=[cos(a),sin(a)];
k=1:160;
plot(ax,800*mod(k*.618,1),600*mod(k*.414,1),'.','Color','#404d57','MarkerSize',2);
% L: orbits, trail, tangent/progress, Saturn rings, capture gate, precision band.
c=["#7dc4ce","#408780","#ffc254","#ccb380","#5ce0c2","#ffc254"];
lw=[1.8 1.2 1.3 2 2 3];
for k=1:6
    s.g.L(k)=plot(ax,nan,nan,'Color',c(k),'LineWidth',lw(k));
end
s.g.L(3).LineStyle=':';
% Shaded 80-by-80 raster discs, generated once; no per-frame texture uploads.
% Earth uses a procedural land mask, with no image files or dependencies.
% Lambertian light from the left: surface normal dot [-0.6,0,0.8].
% A small ambient floor keeps the night side visible; this is visual shading,
% not a calculation of the Sun's actual direction in Saturn's moon system.
x=linspace(-1,1,80); z=max(0,1-x.^2-x'.^2);
c=[.8 .8 .8;.8 .8 .8;.12 .55 .82;.9 .75 .5];
for k=1:4
    rgb=max(.1,.8*sqrt(z)-.6*x).*reshape(c(k,:),1,1,3);
    if k==3, rgb(:,:,3)=rgb(:,:,3).*(1-.7*(sin(8*x)+cos(7*x')>.7)); end
    s.g.I(k)=image(ax,'CData',rgb,'AlphaData',z>0);
end
s.g.ship=patch(ax,nan,nan,'w','EdgeColor','#7dd9db');
% render assigns both button colors, so no duplicate initial color is needed.
s.g.button=plot(ax,[290 510],[42 42],'LineWidth',38);
% T: title, score/clock, journey, action, message, two moon names, gate name.
fs=[22 14 12 19 20 11 11 10];
for k=1:8
    s.g.T(k)=text(ax,0,0,'','FontSize',fs(k), ...
        'Color','#e1eff5','Clipping','on');
end
set(s.g.T(4:7),'HorizontalAlignment','center');
set(s.g.T([2 8]),'HorizontalAlignment','right');
set(ax.Children,'HitTest','off','PickableParts','none');
s=reset(s);
% Warm the solver during setup instead of on the first player's boost.
flight(s);
end

function s=reset(s)
% Keep the pooled graphics. All state is per-round; no score storage is used.
% The first 15 centers form the moon course; center 16 marks the escape gate
% until the ending places Earth. This arrangement is not Saturn's real map.
s.score=0; s.n=1; s.hp=3;
y=[0 repmat([8 -14 9 -14],1,4)];
s.c=[(0:15)'*52+21,40+y(1:16)']; s.c(16,2)=40;
s.a=-2.65; s.p=s.c(1,:)+12*[cos(s.a) sin(s.a)]; s.d=[-sin(s.a) cos(s.a)];
s.m=1; s.t=0; s.t0=0; s.intro=3; 
s.msg='';
s.cam=0; s.v=[0 40 112];
end

function s=tick(s,dt,pressed)
% Absolute mode start times preserve leftover frame time at transitions.
% dt is elapsed time supplied by the harness, not a fixed distance per frame.
% A tap uses the displayed position and tangent before advancing the clock;
% taps during flight or settling do not queue another boost.
if pressed
    if ismember(s.m,[1 8 9])
        s=reset(s); s.m=2; return
    elseif s.m==3
        s.f=flight(s); s.t0=s.t; s.m=4; s.msg='';
    end
end
if s.m==2
    s.intro=max(0,s.intro-dt);
    if s.intro<1e-9, s.m=3; end
    return
end
if ismember(s.m,[1 8 9]), return; end
if s.m==7
    % The one-second homecoming has its own clock, outside the 120-second round.
    s.u=min(1,s.u+dt);
else
    s.t=min(120,s.t+dt);
    if s.m==4
        % Follow the precomputed flight by elapsed time. Interpolation allows
        % render frames to fall between solver samples without re-solving.
        s.ft=min(s.f.t(end),s.t-s.t0);
        p=interp1(s.f.t,s.f.xy,s.ft); d=p-s.p; s.p=p;
        if norm(d)>eps, s.d=d/norm(d); end
        if s.ft>=s.f.t(end)-1e-9, s=land(s,s.t0+s.f.t(end)); end
    end
    if s.m==5
        % Blend into the new orbit in 0.3 s, or recover after a miss in 0.7 s.
        % This capture/recovery aid is not a simulated braking maneuver.
        age=s.t-s.t0; b=ease(age/s.wait);
        target=s.c(s.n,:)+12*[cos(s.a) sin(s.a)];
        s.p=s.from+(target-s.from)*b;
        s.cam=s.cam0+(52*(s.n-1)-s.cam0)*b;
        if age>=s.wait, s.m=3; s.t0=s.t0+s.wait; end
    end
    if s.m==3
        % Prescribed circular orbit; angular speeds are 1.88, 2.06, 2.24 rad/s.
        % r = center + 12*[cos(theta),sin(theta)], theta = anchor + omega*time.
        % [-sin(theta),cos(theta)] is the counterclockwise unit tangent.
        % Radius and angular speed are game settings, not Keplerian solutions;
        % the boost replaces orbital velocity with 58 units/s along the tangent.
        a=s.a+(1.7+.18*ceil(s.n/5))*(s.t-s.t0);
        s.p=s.c(s.n,:)+12*[cos(a) sin(a)]; s.d=[-sin(a) cos(a)];
    end
    if s.t>=120 && s.m~=7, s.m=9; s.msg='TIME IS UP'; end
end
s.v=[s.cam 40 112];
if ismember(s.m,[7 8])
    s.p=s.o+[160*ease(s.u) 0];
    s.v=[s.o(1)-70 s.o(2) 276];
    if s.u>=1, s.m=8; s.n=16; end
end
end

function g=gates(s,t)
% Every five moons narrow the gate and increase its vertical motion.
% g=[x,y,half-width]. Gate motion is a timing challenge, not moon motion.
tier=ceil(s.n/5);
g=[s.c(s.n+1,:)+[-12 0],13-.5*tier];
g(2)=g(2)+.75*(tier-1)*sin(.75*t+s.n+1);
end

function f=flight(s)
% Integrate position and velocity: dr/dt=v, dv/dt=gravity(r).
% Current and up to two upcoming moons attract the ship; their centers stay
% fixed. Saturn/Sun gravity and moving-moon energy exchange are omitted.
% A real gravity assist exchanges energy with a moving moon or planet in the
% larger reference frame. Here the boost sets speed, and gravity bends flight.
% ode45 chooses adaptive integration steps; deval samples at 1/60-second
% intervals for playback. These samples do not require a 60-fps renderer.
% Flights end at the next gate plane (before the target surface), or at 4.5 s.
% A missed gate costs a shield; no physical collision response is simulated.
c=s.c(s.n:min(15,s.n+2),:); g=gates(s,s.t);
p=s.p; v=58*s.d;
opt=odeset('RelTol',2e-5,'AbsTol',1e-7,'MaxStep',.1,'Events',@(t,y)plane(y,g(1)));
sol=ode45(@(t,y)gravity(y,c),[0 4.5],[p v]',opt);
d=4.5; hit=0; q=inf;
if ~isempty(sol.xe)
    % Evaluate the moving gate at crossing time, not at launch time.
    % q is vertical error divided by gate half-width; q<=1 is a capture.
    d=sol.xe(end); moving=gates(s,s.t+d);
    q=abs(sol.ye(2,end)-moving(2))/moving(3);
    hit=(s.n+1)*(q<=1);
end
t=unique([0:1/60:d,d]); xy=deval(sol,t);
f=struct('t',t,'xy',xy(1:2,:)','hit',hit,'q',q);
end

function dy=gravity(y,c)
% y=[x;y;vx;vy]. Each row of delta points from the ship toward a moon.
% a = sum(mu*delta/(|delta|^2+epsilon^2)^(3/2)), mu=112, epsilon=2.
% Far from a moon this approaches Newtonian inverse-square acceleration.
% Softening keeps acceleration finite near its center and eases integration.
% All moons share the same tuned mu (the role of G*mass); positions, speeds,
% and distances use game units, not measured Saturn-system values.
delta=c-y(1:2)';
dy=[y(3:4);sum(112*delta./(sum(delta.^2,2)+4).^1.5,1)'];
end

function [v,k,d]=plane(y,x)
% Stop at a left-to-right gate crossing: zero value, terminal, direction +1.
% ode45 may request only the value, or value/terminal/direction together.
v=y(1)-x; k=1; d=1;
end

function s=land(s,at)
% Resolve a gate crossing or flight timeout; at is the exact flight end time.
% The center third scores 200; other captures score 100. Escape adds 1000.
f=s.f; s.t0=at; s.from=s.p; s.cam0=s.cam;
if f.hit<=0
    s.hp=s.hp-1; s.m=5; s.wait=.7; s.a=-2.65;
    s.msg='MISSED ORBIT';
    if s.hp==0, s.m=9; s.msg='SIGNAL LOST'; end
else
    perfect=f.q<=1/3; points=100*(1+perfect);
    s.score=s.score+points;
    s.msg=sprintf('CAPTURE +%d',points);
    if perfect, s.msg=sprintf('PERFECT +%d',points); end
    if f.hit==16
        % Narrative escape and a one-second straight Earth animation, not an
        % escape-velocity calculation or a real interplanetary transfer.
        % The moon course and escape gate symbolically represent leaving
        % Saturn's sphere of influence; no physical boundary is calculated.
        % Passing the last moon is not that boundary, and Saturn's gravity
        % does not abruptly disappear beyond its sphere of influence.
        s.score=s.score+1000; s.m=7;
        s.u=max(0,s.t-at); s.t=min(120,at);
        s.o=s.p; s.c(16,:)=s.p+[172 0];
    else
        s.n=f.hit; d=s.p-s.c(s.n,:); s.a=atan2(d(2),d(1));
        s.wait=.3; s.m=5;
    end
end
end

function q=ease(q)
% Smoothstep for assisted capture/camera motion, not gravitational acceleration.
% 3*q^2-2*q^3 has zero slope at both ends, avoiding abrupt animation stops.
q=min(1,max(0,q)); q=q*q*(3-2*q);
end

function p=screen(p,s)
% Map game coordinates to the fixed 800-by-600 axes; only the viewport moves.
p=(p-s.v(1:2))*(720/s.v(3))+[40 300];
end

function draw(~,s)
% Pure presentation: fixed axes, pooled graphics, no state mutation/drawnow.
h=s.g; home=ismember(s.m,[7 8]); scale=720/s.v(3);
circles=nan(132,2);
for k=1:2
    node=s.n+k-1; on=~home && node<16 && s.m~=2;
    show([h.I(k),h.T(k+5)],on);
    if ~on, continue; end
    c=s.c(node,:); body(h.I(k),screen(c,s),5.3*scale);
    label(h.T(k+5),char(upper(s.names(node))),screen(c-[0 16.5],s));
    circles((k-1)*66+(1:65),:)=screen(c+12*s.arc,s);
end
stroke(h.L(1),circles); show(h.I(3),home);
d=s.d; trail=zeros(0,2); aim=zeros(0,2);
sat=[s.cam+100 67]; r=5;
if ismember(s.m,[4 5]), trail=screen(s.f.xy(s.f.t<=s.ft,:),s); end
% The dotted guide is a release tangent, not a guaranteed trajectory prediction.
if s.m==3, aim=screen([s.p;s.p+28*d],s); end
show([h.L(5),h.L(6),h.T(8)],~home && s.m~=2);
if home
    sat=s.o+[-30 0]; r=12; d=[1 0];
    body(h.I(3),screen(s.c(16,:),s),7*scale);
    show(h.T(6),true); label(h.T(6),'EARTH',screen(s.c(16,:)-[0 13],s));
    trail=screen([sat+[27 0];s.c(16,:)-[7 0]],s);
    aim=screen([s.o;s.p],s);
else
    g=gates(s,s.t); x=g(1); y=g(2); w=g(3); name='CAPTURE';
    if s.n==15, name='ESCAPE'; end
    stroke(h.L(5),screen([x-1 y-w;x y-w;x y+w;x-1 y+w],s));
    stroke(h.L(6),screen([x y-w/3;x y+w/3],s));
    label(h.T(8),name,screen([x-1 y-w-6],s));
end
stroke(h.L(2),trail); stroke(h.L(3),aim);
body(h.I(4),screen(sat,s),r*scale);
stroke(h.L(4),screen(sat+r*(s.arc.*[2 .6]),s));
p=screen([2 0;-1 -.8;-1 .8]*[d;-d(2) d(1)]+s.p,s);
put(h.ship,'XData',p(:,1),'YData',p(:,2));
show([h.I(4),h.L(1:4),h.ship],s.m~=2);
msg=s.msg;
if s.m==1, msg={'ESCAPE SATURN''S','SPHERE OF INFLUENCE'}; end
if s.m==2, msg=sprintf('GOING HOME\n\nEscape Saturn''s sphere of influence.\nReach Earth.\n\n%d',max(1,ceil(s.intro))); end
if home
    msg='SATURN ESCAPED / GOING HOME';
    if s.m==8, msg='HOME AT LAST'; end
end
label(h.T(5),msg,[400 474-174*(s.m==2)]);
label(h.T(1),'SLINGSHOT HOME',[28 568]);
label(h.T(2),sprintf('SCORE %06d   %05.1fs',s.score,120-s.t),[772 568]);
label(h.T(3),sprintf('%02d/15 / %s   SHIELDS %d',min(15,s.n),upper(s.names(s.n)),s.hp),[28 530]);
labels={'Launch','Get Ready','Boost','Coasting','Settling','','Going Home','Play Again','Try Again'};
label(h.T(4),labels{s.m},[400 36]);
on=ismember(s.m,[1 3 8 9]);
% Amber signals an available action; switch the label contrast with its fill.
put(h.button,'Color',[.14 .19 .21]+on*[.86 .57 .12]);
put(h.T(4),'Color',[.88 .94 .96]-.8*on);
end

function stroke(h,p)
put(h,'XData',p(:,1)','YData',p(:,2)');
end

function body(h,c,r)
% Position a cached raster disc using its center and bounding radius.
stroke(h,c+[-r r;r -r]);
end

function label(h,value,p)
put(h,'String',value,'Position',[p 0]);
end

function show(h,on)
set(h,'Visible',on);
end

function put(h,varargin)
% Unchanged properties stay untouched, keeping static planets inexpensive.
for k=1:2:numel(varargin)
    if ~isequal(get(h,varargin{k}),varargin{k+1}), set(h,varargin{k},varargin{k+1}); end
end
end
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Preview

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