3D scenes
Each block is the whole file — copy it into x.manic and run manic x.manic (live) or --record out (video). See the Going 3D chapter for the words used here.
three_d
Cubes, spheres, arrows, a curve, a surface and solids together — the 3D basics on one stage.
title("3D coordinate space");
canvas(1280, 720);
template("terminal");
camera3((8, -10, 6), (0, 0, 1), 45);
grid3(floor, (0, 0, 0), 5, 1);
color(floor, dim);
axes3(world, (0, 0, 0), 4);
cube3(box, (0, 0, 1), (2, 2, 2));
color(box, magenta);
sphere3(ball, (-2, 1, 1), 0.7);
color(ball, lime);
arrow3(vector, (0, 0, 0), (2.5, 2, 3));
// a parametric helix (curve3), drawn on as a shaded tube
curve3(spiral, "cos(t)*2.6", "sin(t)*2.6", "t*0.32", (0, 12));
color(spiral, gold);
thick(spiral, 0.08);
// a height-field surface z = f(x,y) (surface3), filled + flat-shaded
surface3(wave, "0.6*sin(x)*cos(y)", (-3.5, 3.5), (-3.5, 3.5), 24);
color(wave, magenta);
opacity(wave, 0.5);
// filled, flat-shaded solids (prism3 / pyramid3)
prism3(hex, (-3.6, -2.4, 1.2), 6, 0.9, 2.2);
pyramid3(cone, (3.6, -2.4, 1.4), 22, 1.0, 2.6);
// a 2D label glued to the moving sphere — tracks it as the camera orbits
text(balltag, (0, 0), "ball");
color(balltag, gold);
pin3(balltag, ball);
par {
rotate3(box, (0, 0, 360), 4, linear);
orbit3(70, 28, 11, 4, smooth);
move3(ball, (2, -1, 2), 4, inout);
}
solids3
Filled, shaded solids: a prism, a cone, and a lathed vase.
title("3D solids");
canvas(1280, 720);
template("terminal");
camera3((9, -11, 7), (0, 0, 1), 45);
grid3(floor, (0, 0, 0), 6, 1);
color(floor, dim);
axes3(world, (0, 0, 0), 3);
// hexagonal prism
prism3(hex, (-4, 0, 1.2), 6, 1.1, 2.4);
color(hex, cyan);
// a cone (a pyramid with many sides)
pyramid3(cone, (0, 0, 1.4), 28, 1.2, 2.8);
color(cone, magenta);
// a lathed vase: radius profile r(t) swept around the vertical axis
revolve3(vase, (4, 0, 1.5), "0.7 + 0.45*sin(t*2.4)", (0, 3), 32);
color(vase, gold);
orbit3(60, 24, 17, 6, smooth);
param3
Parametric surfaces a height field can’t make — a torus, a sphere, and a Möbius strip.
// param3 — general parametric surfaces x(u,v), y(u,v), z(u,v). Unlike surface3
// (a height field z=f(x,y)) these can wrap and close, so a torus and a Möbius
// strip are just three formulas each.
//
// manic examples/param3.manic
// manic examples/param3.manic --record out --fps 60
title("parametric surfaces");
canvas("16:9");
template("terminal");
camera3((11, -13, 8.5), (0, 0, 1.4), 42);
grid3(floor, (0, 0, 0), 7, 1);
color(floor, dim);
// torus (left)
param3(torus,
"0 - 4.8 + (2 + 0.7*cos(v))*cos(u)",
"(2 + 0.7*cos(v))*sin(u)",
"1.5 + 0.7*sin(v)",
(0, 6.283), (0, 6.283), 40);
color(torus, cyan);
// parametric sphere (centre)
param3(ball,
"1.3*sin(v)*cos(u)",
"1.3*sin(v)*sin(u)",
"1.6 + 1.3*cos(v)",
(0, 6.283), (0, 3.1416), 28);
color(ball, magenta);
// Möbius strip (right)
param3(mobius,
"4.8 + (1.7 + v*cos(u/2))*cos(u)",
"(1.7 + v*cos(u/2))*sin(u)",
"1.6 + v*sin(u/2)",
(0, 6.283), (0 - 0.6, 0.6), 60);
color(mobius, gold);
show(floor, 0.3);
par { show(torus, 0.7); show(ball, 0.7); show(mobius, 0.7); }
orbit3(60, 24, 15, 5.0, smooth);
wait(0.4);
extrude3
Lifting flat shapes into solids, including a boolean cut-out (a plate with a hole) and an L-beam.
// Extrude & CSG — turn 2D shapes into 3D solids. `extrude3` sweeps any 2D
// fillable shape (or a boolean region) straight up; extruding a union/
// difference/intersect gives constructive-solid-geometry solids. The 2D
// source shapes are auto-hidden — they're just the cross-section recipe.
//
// manic examples/extrude3.manic
// manic examples/extrude3.manic --record out --fps 60
title("Extrude & CSG");
canvas(1280, 720);
template("terminal");
camera3((9, -11, 7), (0, 0, 0.8), 45);
grid3(floor, (0, 0, 0), 6, 1);
color(floor, dim);
axes3(world, (0, 0, 0), 3);
// CSG: a square plate MINUS a circular hole → an extruded plate-with-a-hole
rect(plate, (0, 0), 3, 3);
circle(hole, (0, 0), 0.9);
difference(cut, plate, hole);
extrude3(block, cut, 1.0, (-3.5, 0, 0.6));
color(block, cyan);
// arbitrary concave polygon: a union of two rects → an L-beam, extruded
rect(la, (0, 0), 2.4, 0.8);
rect(lb, (-0.8, 0.8), 0.8, 2.4);
union(lshape, la, lb);
extrude3(ell, lshape, 0.9, (3.5, 0, 0.55));
color(ell, magenta);
// a plain shape extrudes just as happily (a hexagon via a sector sweep)
sector(hexface, (0, 0), 1.2, 0, 360);
extrude3(disc, hexface, 0.5, (0, 3.5, 0.3));
color(disc, gold);
orbit3(60, 24, 17, 8, smooth);
morph3
Morphing across families — a cube into a sphere, a saddle into a bowl, a helix into a ring.
// 3D morphing (morph3) — set a 3D entity up to become another shape, then
// blend with `to(id, morph, 1, dur)`. Works across three families:
// • solids — a cube becomes a sphere (reparameterised spherically)
// • surfaces — a rippling saddle settles into a bowl (filled + shaded)
// • curves — a helix unwinds into a flat ring
//
// manic examples/morph3.manic
// manic examples/morph3.manic --record out --fps 60
title("3D morph");
canvas("16:9");
template("terminal");
camera3((11, -13, 8), (0, 0, 0.8), 42);
grid3(floor, (0, 0, 0), 7, 1);
color(floor, dim);
// solid: cube -> sphere
cube3(box, (-5, 0, 1.4), (2.4, 2.4, 2.4));
color(box, cyan);
sphere3(ball, (0, 0, 0), 1.5);
hidden(ball);
morph3(box, ball);
// surface: rippling saddle -> smooth bowl
surface3(saddle, "0.8*sin(x*1.3)*cos(y*1.3)", (-2.3, 2.3), (-2.3, 2.3), 24);
color(saddle, gold);
surface3(bowl, "0.16*(x*x + y*y) - 1", (-2.3, 2.3), (-2.3, 2.3), 24);
hidden(bowl);
morph3(saddle, bowl);
// curve: helix -> flat ring
curve3(helix, "5 + 1.5*cos(t)", "1.5*sin(t)", "0.2*t", (0, 18));
color(helix, magenta);
thick(helix, 0.06);
curve3(ring, "5 + 1.5*cos(t)", "1.5*sin(t)", "1.8", (0, 6.283));
hidden(ring);
morph3(helix, ring);
show(floor, 0.3);
par { show(box, 0.5); show(saddle, 0.5); show(helix, 0.5); }
wait(0.7);
par {
to(box, morph, 1, 3.0, smooth);
to(saddle, morph, 1, 3.0, smooth);
to(helix, morph, 1, 3.0, smooth);
orbit3(48, 25, 21, 3.0, smooth);
}
wait(0.8);
matrix3
A 3×3×3 block of cubes, with a shear matrix M and its inverse M⁻¹ applied and undone.
// A 3 × 3 × 3 block of 27 cubes, then a matrix operation: a 3×3 matrix is a
// linear map of space. We apply a shear M to every cell, then its inverse
// M^-1 — which sends the block back exactly, because M^-1 M = I.
//
// manic examples/matrix3.manic
// manic examples/matrix3.manic --record out --fps 60
title("3 × 3 × 3 · M and M^-1");
canvas("16:9");
template("terminal");
camera3((7.5, -9, 6), (2.4, 0, 2.1), 42);
grid3(floor, (0, 0, 0), 6, 1);
color(floor, dim);
let s = 1.3; // cell spacing (cubes are 1 wide → 0.3 gaps)
let zc = 2.1; // height of the block's centre
let a = 0.7; // shear amount: M sends x → x + a·z
text(cap, (cx, h - 42), "");
display(cap); color(cap, fg); size(cap, 21); hidden(cap);
// --- 27 cubes, three x-slices coloured cyan / magenta / lime ---
for j in 0..3 { for k in 0..3 {
cube3(xa{j}{k}, (0 - s, (j - 1)*s, zc + (k - 1)*s), (1, 1, 1));
color(xa{j}{k}, cyan); hidden(xa{j}{k});
} }
for j in 0..3 { for k in 0..3 {
cube3(xb{j}{k}, (0, (j - 1)*s, zc + (k - 1)*s), (1, 1, 1));
color(xb{j}{k}, magenta); hidden(xb{j}{k});
} }
for j in 0..3 { for k in 0..3 {
cube3(xc{j}{k}, (s, (j - 1)*s, zc + (k - 1)*s), (1, 1, 1));
color(xc{j}{k}, lime); hidden(xc{j}{k});
} }
// --- the matrices, as monospace text on the right ---
text(mLabel, (995, 232), "M =");
text(m0, (1035, 274), "[ 1 0 0.7 ]");
text(m1, (1035, 310), "[ 0 1 0 ]");
text(m2, (1035, 346), "[ 0 0 1 ]");
text(iLabel, (995, 446), "M^-1 =");
text(i0, (1035, 488), "[ 1 0 -0.7 ]");
text(i1, (1035, 524), "[ 0 1 0 ]");
text(i2, (1035, 560), "[ 0 0 1 ]");
display(mLabel); display(m0); display(m1); display(m2);
display(iLabel); display(i0); display(i1); display(i2);
color(mLabel, cyan); color(m0, cyan); color(m1, cyan); color(m2, cyan);
color(iLabel, gold); color(i0, gold); color(i1, gold); color(i2, gold);
size(mLabel, 24); size(m0, 22); size(m1, 22); size(m2, 22);
size(iLabel, 24); size(i0, 22); size(i1, 22); size(i2, 22);
hidden(mLabel); hidden(m0); hidden(m1); hidden(m2);
hidden(iLabel); hidden(i0); hidden(i1); hidden(i2);
// ------------------------------ script ------------------------------
show(floor, 0.3);
show(cap, 0.3);
say(cap, "A 3 by 3 by 3 block — 27 cells.", 0.7);
stagger(0.04) {
for j in 0..3 { for k in 0..3 { show(xa{j}{k}, 0.3); } }
for j in 0..3 { for k in 0..3 { show(xb{j}{k}, 0.3); } }
for j in 0..3 { for k in 0..3 { show(xc{j}{k}, 0.3); } }
}
orbit3(38, 22, 13, 1.6, smooth);
say(cap, "A 3×3 matrix M is a linear map of space. This M shears x by height z.", 1.0);
stagger(0.12) { show(mLabel, 0.3); show(m0, 0.3); show(m1, 0.3); show(m2, 0.3); }
// apply M: x' = x + a·(z - zc)
par {
for j in 0..3 { for k in 0..3 {
move3(xa{j}{k}, (0 - s + a*(k - 1)*s, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
for j in 0..3 { for k in 0..3 {
move3(xb{j}{k}, (a*(k - 1)*s, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
for j in 0..3 { for k in 0..3 {
move3(xc{j}{k}, (s + a*(k - 1)*s, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
}
say(cap, "Applying M slants the whole block — the higher a cell, the more it shifts.", 1.0);
stagger(0.12) { show(iLabel, 0.3); show(i0, 0.3); show(i1, 0.3); show(i2, 0.3); }
say(cap, "The inverse M^-1 just negates the shear.", 0.8);
// apply M^-1: sends every cell back to where it started
par {
for j in 0..3 { for k in 0..3 {
move3(xa{j}{k}, (0 - s, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
for j in 0..3 { for k in 0..3 {
move3(xb{j}{k}, (0, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
for j in 0..3 { for k in 0..3 {
move3(xc{j}{k}, (s, (j - 1)*s, zc + (k - 1)*s), 1.8, smooth);
} }
}
say(cap, "M^-1 sends every cell home: M^-1 M = I, the identity.", 1.0);
orbit3(70, 26, 13, 2.4, smooth);
wait(0.6);