Shape Transformation

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Shape Transformation Properties Page

The Fractal Science Kit fractal generator Shape Transformation page defines a transformation based on a given shape or a blend of 2 shapes. To transform a point, the input point's angular measure relative to the origin is calculated and a delta value is computed by finding the shape's radial measure for the given angle. The delta is applied to the original point to obtain the transformed value.

See also:

Shape Transformation

Fractal Science Kit - Shape Transformation

The Type field in the Shape Transformation section of the page defines how the shape is defined and can be one of the following values:

  • Shape 1
  • Minimum
  • Maximum
  • Sum
  • Difference
  • Product
  • Quotient
  • Power
  • Arithmetic Mean
  • Geometric Mean
  • Harmonic Mean
  • Quadratic Mean
  • Angle Blend 2
  • Angle Blend 4
  • Angle Blend 6
  • Angle Blend 8
  • Angle Blend 12
  • Dwell Blend 2
  • Dwell Blend 4
  • Dwell Blend 6
  • Dwell Blend 8
  • Dwell Blend 12

If Type is Shape 1 then only the Shape 1 section is enabled and the resulting transformation is based solely on the shape defined in that section. Otherwise, both the Shape 1 and Shape 2 sections are enabled and the resulting transformation is based on a blend of the 2 shapes given by Type. Minimum and Maximum use the shape with the minimum/maximum radial value for a given angle. Sum, Difference, Product, Quotient, and Power, apply the indicated operation to the 2 radial values for a given angle. The various means compute the mean of the 2 radial values for a given angle using the named method. The angle blends divide the complex plane into N sectors, where N is given in the name, and blend the shapes such that Shape 1 is dominant in even sectors and Shape 2 is dominant in odd sectors. Similarly, the dwell blends arrange that Shape 1 and Shape 2 oscillate over a period of N dwells.

Shape 1 / Shape 2

Fractal Science Kit - Shape Transformation

The Shape 1 and Shape 2 sections contain 4 fields: Type, R, N, and S. Each section defines the associated shape used in the transformation blend. Type is the type of shape, R controls the shape's size and equates to the shape's radius unless stated otherwise, N is an integer argument specific to the shape, and S is a floating point argument specific to the shape. R, N, and/or S are enabled as required based on the shape's type. The text of Type contains details as to how R, N, and S are interpreted by the given type.

The following list gives the possible values for each shape's Type:

  • Circle
  • Ellipse (R = x radius, S = y radius)
  • Parabola 1A (R = focal distance)
  • Parabola 1B (R = focal distance)
  • Parabola 2A (R = focal distance)
  • Parabola 2B (R = focal distance)
  • Hyperbola A (R = major axis, S = minor axis)
  • Hyperbola B (R = minor axis, S = major axis)
  • Square
  • Rectangle (height factor S)
  • Triangle A
  • Triangle B
  • Diamond
  • Hexagon A
  • Hexagon B
  • Octagon A
  • Octagon B
  • Astroid (power S)
  • Cardioid A
  • Cardioid B
  • Flower 1A (outer radius R, N petals)
  • Flower 1B (outer radius R, N petals)
  • Flower 2A (inner radius R, N petals)
  • Flower 2B (inner radius R, N petals)
  • Flower 3A (N petals, shape control S)
  • Flower 3B (N petals, shape control S)
  • Flower 4A (N petals, shape control S)
  • Flower 4B (N petals, shape control S)
  • Star 1A (N points, shape control S)
  • Star 1B (N points, shape control S)
  • Star 2A (N points, shape control S)
  • Star 2B (N points, shape control S)
  • Gear A (N points, shape control S)
  • Gear B (N points, shape control S)
  • SuperEllipse (N points, power S)
  • Conic A (N sectors, eccentricity S)
  • Conic B (N sectors, eccentricity S)
  • Cross A
  • Cross B
  • Hyper-Cross A
  • Hyper-Cross B

 

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