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Frost Flower

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❄️ Create a delicate 3D printable snowflake using interpolated curves and 12-fold rotational symmetry! This tutorial demonstrates how smooth B-spline curves and offset operations can create organic, nature-inspired shapes.

The algorithm:

  1. Define branch points - a simple zigzag pattern for one branch
  2. Interpolate a smooth curve - creates flowing organic lines
  3. Rotate 180° the branch to create bilateral symmetry
  4. Combine wires into a single branch pair
  5. Create outer and inner offsets - hollow structure for the branch
  6. Create face from wires - outer and reversed inner wire form a hollow face
  7. Rotate copies at 30° intervals (0°, 30°, 60°, 90°, 120°, 150°) for 12-fold symmetry
  8. Boolean union to merge all faces into one shape
  9. Extrude the unified face to create a 3D solid
Bitbybit Platform

Snowflake ornament

rete logoRete
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How It Works​

Branch Design​

Each branch is defined by 5 points creating a gentle zigzag pattern:

  • Center point at origin (0, 0, 0)
  • Alternating left/right offsets as Y increases (0.3, -0.2, 0.4...)
  • Tip point centered for a clean finish (0, 4*size, 0)

The interpolatePoints operation creates a smooth B-spline curve through these points.

Bilateral Symmetry​

The branch wire is rotated 180° around the Z-axis, creating a mirrored copy. Both wires are then combined into a single wire, forming the classic "double-branched" snowflake arm look.

Creating Hollow Structure​

Instead of solid geometry, this creates a delicate hollow branch:

  1. Outer offset: The combined wire is offset outward by 0.4 units
  2. Inner offset: The combined wire is offset outward by 0.2 units, then reversed (direction flipped)
  3. Face from wires: The outer and reversed inner wire create a face with a hollow center - like a ribbon

12-Fold Symmetry​

The hollow face is rotated at 30° intervals (0°, 30°, 60°, 90°, 120°, 150°), creating 6 rotated copies plus the original. This creates a complex 12-branch pattern when the bilateral branches overlap, giving the appearance of intricate snowflake geometry.

Final 3D Solid​

  1. Boolean Union: All rotated faces are merged into a single flat 2D shape
  2. Extrude: The unified shape is extruded 0.2 units along the Z-axis to create the final 3D printable solid

Customization ❄️​

  • Size slider: Scale the entire snowflake (controls the Y coordinates of branch points)
  • Offset distances: Adjust the 0.4 and 0.2 values to change the branch thickness
  • Edit point positions: Modify the zigzag pattern for different branch styles
  • Rotation angles: Change the 30° step to create different symmetries (try 60° for 6-fold, or 45° for 8-fold)

3D Printing Tips​

  • The offset technique creates thin, elegant branches - great for decorative ornaments
  • The boolean union creates a single manifold mesh - no intersecting geometry!
  • 0.1-0.15mm layer height for fine detail
  • 10-15% infill (it's mostly thin walls anyway)
  • White or translucent filament for icy look
  • Consider adding a small cylinder at the center for a hanging hole

Happy holidays! ❄️