Parametric three dimensional grid of spheres and rods used for teaching crystal lattice geometry and spatial repetition

// cubic lattice model
// Parametric three dimensional grid of spheres and rods used for teaching crystal lattice geometry and spatial repetition
// Categories: Maker

// units
@settings(defaultLengthUnit = mm)

// project title
projectTitle = "cubic lattice ball and stick model"

// project description
projectDescription = "parametric three dimensional grid of spheres and rods used for teaching crystal lattice geometry and spatial repetition"

// parameters
gridInstancesPerAxis = 3
gridSpacingLength = 20
nodeSphereRadiusLength = 5
rodCylinderRadiusLength = 0.5
rodExtrudeLengthY = 2 * gridSpacingLength
nodeColorHexadecimal = "#ff0059"
rodColorHexadecimal = "#00fffb"

// node sphere
nodeSketchPlane = startSketchOn(XZ)
nodeProfile = startProfile(nodeSketchPlane, at = [0, -nodeSphereRadiusLength])
  |> yLine(length = 2 * nodeSphereRadiusLength)
  |> arc(interiorAbsolute = [nodeSphereRadiusLength, 0], endAbsolute = [profileStartX(%), profileStartY(%)])
  |> close()
nodeSphereSolid = revolve(nodeProfile, angle = 360deg, axis = Y)
appearance(nodeSphereSolid, color = nodeColorHexadecimal)

// nodes pattern
nodesPatternAlongX = patternLinear3d(
  nodeSphereSolid,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = X,
)
nodesPatternAlongXThenY = patternLinear3d(
  nodesPatternAlongX,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = Y,
)
nodesPatternAlongXThenYThenZ = patternLinear3d(
  nodesPatternAlongXThenY,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = Z,
)

// rods
rodYSketchPlane = startSketchOn(XZ)
rodYProfile = circle(rodYSketchPlane, center = [0, 0], radius = rodCylinderRadiusLength)
rodYCylinder = extrude(rodYProfile, length = -rodExtrudeLengthY)
appearance([rodYCylinder], color = rodColorHexadecimal)

rodsAlongYPatternAlongX = patternLinear3d(
  rodYCylinder,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = X,
)
rodsAlongYPatternAlongXThenZ = patternLinear3d(
  rodsAlongYPatternAlongX,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = Z,
)

rodsAlongX = clone(rodsAlongYPatternAlongXThenZ)
  |> rotate(axis = Z, angle = 90)
  |> translate(x = rodExtrudeLengthY, global = true)

rodsAlongZ = clone(rodsAlongYPatternAlongXThenZ)
  |> rotate(axis = X, angle = 90, global = true)
  |> translate(y = rodExtrudeLengthY, global = true)


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lattice-cubic