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
nodeProfile = sketch(on = XZ) {
  line1 = line(start = [var 0mm, var -5mm], end = [var 0mm, var 5mm])
  arc2 = arc(start = [var 0mm, var 5mm], end = [var 0mm, var -5mm], center = [var 0mm, var 0mm])
  coincident([line1.end, arc2.start])
  coincident([line1.start, arc2.end])
  coincident([arc2.center, ORIGIN])
  coincident([line1, arc2.center])
  vertical(line1)
  distance([line1.start, line1.end]) == 2 * nodeSphereRadiusLength
  radius(arc2) == nodeSphereRadiusLength
}
nodeRegion = region(segments = [nodeProfile.line1])
nodeSphereSolid = revolve(nodeRegion, angle = 360deg, axis = Y)
hide(nodeProfile)
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
rodSketchOffset = 0.001mm
rodSketchPlane = offsetPlane(XZ, offset = rodSketchOffset)
rodYProfile = sketch(on = rodSketchPlane) {
  circle1 = circle(start = [var 0.5mm, var 0mm], center = [var 0mm, var 0mm])
  coincident([circle1.center, ORIGIN])
  distance([circle1.center, circle1.start]) == rodCylinderRadiusLength
}
rodYRegion = region(segments = [rodYProfile.circle1])
rodYCylinder = extrude(rodYRegion, length = -rodExtrudeLengthY)
  |> translate(y = -rodSketchOffset, global = true)
hide(rodYProfile)
appearance([rodYCylinder], color = rodColorHexadecimal)

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

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

rodsAlongXPatternAlongY = patternLinear3d(
  rodXCylinder,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = Y,
)
rodsAlongX = patternLinear3d(
  rodsAlongXPatternAlongY,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = Z,
)

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

rodsAlongZPatternAlongX = patternLinear3d(
  rodZCylinder,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = X,
)
rodsAlongZ = patternLinear3d(
  rodsAlongZPatternAlongX,
  instances = gridInstancesPerAxis,
  distance = gridSpacingLength,
  axis = [0, -1, 0],
)


cubic lattice model

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