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Temari Ball 7: Spherical motif from circles and sequences

Temari Ball 7: Spherical motif from circles and sequences
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2020-09-03 15:15
CircleSequenceSolid GeometryGeometric ConstructionLocus
This example demonstrates how to generate a Temari-ball–style ornamental pattern on a sphere by repeating a motif with controlled sampling. The key concepts are spherical geometry (Sphere), geometric circle construction (Circle), and parameter-controlled iteration using a sequence (Sequence) to build structured repetitions. Construction-wise, Circle and Sequence are used to create and iterate a set of circle-based elements (points/sections or motif-defining features), and Sphere is then used to place the resulting geometry onto a 3D spherical surface. The construction objects (e.g., O as the center, R as the radius, and parameter variables such as k, motif, m, n, a, p, b, along with list objects like liste1–liste7 and intermediate images image1–image3) indicate how the repeated pattern pieces are organized into a coherent surface/curve visualization. Suitable for middle-school to pre-university geometry visualization and for workshops on parametric/iterative geometric construction and 3D graphing in GeoGebra.

GeoGebra Commands & Parameters

  1. Circle(O, R, xOyPlane) → c
  2. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste1
  3. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) - (R * sin(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste2
  4. Sequence(CurveCartesian[x(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste4
  5. Sequence(CurveCartesian[x(O) - (R * sin(i - (π / ((2 * n)) * ff((m * t))))), y(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste5
  6. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) + (R * sin(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste6
  7. Sequence(CurveCartesian[x(O) + ((R * cos(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), y(O) - (R * sin(i - (π / ((2 * n)) * ff((m * t))))), z(O) + ((R * sin(t)) * cos(i - (π / ((2 * n)) * ff((m * t))))), t, 0, 6.28319], i, -1.5708, 3.141592653589793, π / n) → liste7
  8. Sphere(O, R - 0.05) → d

AI Drawing Prompt Reference

Draw a Temari ball-style ornamental pattern on a sphere by repeating a motif controlled by circles and sequences. Start by creating a circle in a plane, then use sequences to iterate and generate multiple curves on the sphere's surface, rotating around the center to form a complex spherical pattern. Combine these curves into a cohesive spherical decoration, showcasing the effects of spherical geometry and parametric iteration.
The prompt above was compiled from the original drawing commands and is for reference only.