9.2 3D Primitives and Transforms

Step 1 — pick the function: We want a cube, so we use cube.

Step 2 — set the size: The edge length is 4, so size: 4.

Step 3 — write the call:

Answer: cube({ size: 4 }) creates a cube with edge length 4 centered at [0,0,0].

Step 1 — pick the function: We need different dimensions, so we use cuboid.

Step 2 — set the size array: Width 6, depth 2, height 8 gives size: [6, 2, 8].

Step 3 — write the call:

Answer: cuboid({ size: [6, 2, 8] }) creates a box 6 wide, 2 deep, and 8 tall.

Step 1 — pick the function: We want a sphere, so we use sphere.

Step 2 — set the radius: The radius is 3, so radius: 3.

Step 3 — write the call:

Answer: sphere({ radius: 3 }) creates a sphere with radius 3 centered at the origin.

Step 1 — pick the function: We want a cylinder, so we use cylinder.

Step 2 — set the options: Height 5 and radius 2 give { height: 5, radius: 2 }.

Step 3 — write the call:

Answer: cylinder({ height: 5, radius: 2 }) creates a cylinder 5 tall with radius 2.

Step 1 — pick the function: We want a donut, so we use torus.

Step 2 — set the radii: The tube radius is innerRadius: 2, and the ring radius is outerRadius: 10.

Step 3 — write the call:

Answer: torus({ innerRadius: 2, outerRadius: 10 }) creates a donut with a tube radius of 2 and a ring radius of 10.

Step 1 — pick the function: We want a box with rounded edges, so we use roundedCuboid.

Step 2 — set the options: The size array is [8, 4, 6] and the round radius is 1, giving { size: [8, 4, 6], roundRadius: 1 }.

Step 3 — write the call:

Answer: roundedCuboid({ size: [8, 4, 6], roundRadius: 1 }) creates a box 8 wide, 4 deep, and 6 tall with rounded edges of radius 1.

Step 1 — pick the function: We want a cylinder with rounded ends, so we use roundedCylinder.

Step 2 — set the options: Height 6, radius 3, and round radius 0.5 give { height: 6, radius: 3, roundRadius: 0.5 }.

Step 3 — write the call:

Answer: roundedCylinder({ height: 6, radius: 3, roundRadius: 0.5 }) creates a cylinder 6 tall with radius 3 and rounded ends.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5].

Step 2 — pick the transform. We are moving the solid, so we use translate.

Step 3 — pass the offset and the solid. The offset is [5, 0, 3] (5 right, 0 deep, 3 up), and the solid comes second.

Answer: translate([5, 0, 3], cuboid({ size: [10, 20, 5] })) — the box shifted 5 units right and 3 units up.

You should see the box tipped a quarter turn around the x axis, so the axis that used to point up now points sideways. In 2D this rotation did nothing because the shape had no thickness there; the box's depth is what lets it tip over. Change the angle to Math.PI and run again to flip it all the way upside down.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5].

Step 2 — pick the transform. We are turning the solid, so we use rotate.

Step 3 — pass the angles and the solid. A quarter turn is Math.PI / 2 radians around the x axis, so the angles are [Math.PI / 2, 0, 0].

Answer: rotate([Math.PI / 2, 0, 0], cuboid({ size: [10, 20, 5] })) — the box tipped a quarter turn around the x axis.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5].

Step 2 — pick the transform. We are resizing the solid, so we use scale.

Step 3 — pass the factors and the solid. Doubling the width means an x factor of 2; tripling the height means a z factor of 3; the depth stays 1.

Answer: scale([2, 1, 3], cuboid({ size: [10, 20, 5] })) — the box now 20 wide, 20 deep, and 15 tall.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5]. We also pass center: [5, 0, 0] so the box starts off-centre and the mirror visibly moves it.

Step 2 — pick the transform. We are flipping the solid, so we use mirror.

Step 3 — set the mirror plane. Flipping across the y-z plane means the plane's normal points along x, so normal: [1, 0, 0].

Answer: mirror({ normal: [1, 0, 0] }, cuboid({ size: [10, 20, 5], center: [5, 0, 0] })) — the box flipped from [5, 0, 0] to [-5, 0, 0].

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5]. We also pass center: [12, 8, 3] so the box starts off-centre and the centering visibly moves it.

Step 2 — pick the transform. We are centering the solid, so we use center.

Step 3 — set the axes. We want to center on all three axes, so axes: [true, true, true].

Answer: center({ axes: [true, true, true] }, cuboid({ size: [10, 20, 5], center: [12, 8, 3] })) — the box slides from [12, 8, 3] to sit centered on the origin.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5]. We also pass center: [12, 8, 3] so the box starts off-centre and the aligning visibly moves it.

Step 2 — pick the transform. We are aligning the solid, so we use align.

Step 3 — set the modes. We want the low edge on z, so the z mode is min; the x and y modes can stay center.

Answer: align({ modes: ['center', 'center', 'min'] }, cuboid({ size: [10, 20, 5], center: [12, 8, 3] })) — the box's low edge slides down to the x-y plane.

You should see the box tipped a quarter turn around x, then slid 5 units to the right. Read it from the inside out: the innermost call (rotate) runs first, then translate wraps the result. Reverse the order — rotate([Math.PI / 2, 0, 0], translate([5, 0, 0], myshape)) — and run again: the box moves first, then the moved box spins around the origin, landing somewhere completely different.

Step 1 — build the shape. We need a box, so we use cuboid with size: [10, 20, 5].

Step 2 — read the order from the inside out. We want to rotate first, then move, so the rotate call is the inner argument and translate wraps it.

Step 3 — write the call. The rotation is Math.PI / 2 around x, and the move is [5, 0, 0].

Answer: translate([5, 0, 0], rotate([Math.PI / 2, 0, 0], cuboid({ size: [10, 20, 5] }))) — the box tips a quarter turn around x, then slides 5 units right.