Inversion Type Variations

Variations that invert across various shapes, such as the unit circle.

Inversion Sample Flames

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d_spherical

Combines spherical and linear.

Type: 2D
Author: Tatyana Zabanova (tatasz)
Date: 5 Jun 2017

Parameter	Description
d_spher_weight	Weight of spherical vs linear; 0 is all linear, 1 is all spherical, 0.5 is half and half; should be between 0 and 1

https://www.deviantart.com/tatasz/art/Utilities-Plugin-Pack-684337906

inversion

Generalizes 2D circle inversion; same as spherical with the default parameters.

Type: 2D
Author: Gregg Helt (CozyG)
Date: 2017

Like spherical, but adds five additional features: shapes besides the standard circle, restricted inversion, alternative p-norms, including the inversion shape and/or original points in the result, and direct coloring.

Parameter	Description
scale	How much the shape is scaled; for a standard circle (shape 0), this is the radius of the inversion
rotation	How much the shape is rotated; 0.5 for 90°, 1 for 180°, etc.
shape	The shape to invert across, one of the following: 0: circle 1: ellipse 2: hyperbola 3: regular polygon 4: rhodonea 5: superellipse 6: supershape
imode	Restricted inversion mode: 0: standard (not restricted) 1: invert only external points (outside the shape) 2: invert only internal points (inside the shape)
hide_uninverted	Hide uninverted points if 1 (true) (has no effect when imode is 0)
a – f	Parameters to control the selected shape (depends on shape): circle: (not used) ellipse: a, b (x and y radii) hyperbola: a, b (x and y radii) regular polygon: n (number of sides) rhodonea: numerator of k, denominator of k, c superellipse: a, b, n supershape: a, b, m, n1, n2, n3
ring_mode	Restrict inversion to a ring: 0: no ring restriction 1: invert only points inside the ring 2: invert only points outside the ring
ring_scale	Controls the size of the restriction ring. It must be something besides 1 to enable ring mode. If scale ≥ 1, set smaller than 1; smaller values increase ring size. If scale ≤ 1, set larger than 1; larger values increase ring size.
pnorm_point	The p-norm for the input point (2 for standard Euclidean distance)
pnorm_shape	The p-norm for the shape boundary point (2 for standard Euclidean distance)
pnorm_pmod	Modifier for the input point; it changes the width of the inversion. Smaller values make it thicker, smaller values thinner. Normally between 0 and 2.
pnorm_smod	Modifier for the shape boundary point; it changes the distance of the inversion from the shape. Smaller values put it further away, larger values bring it closer (possibly past the boundary).
draw_shape	Relative density of shape outline to the inversion, between 0 (don’t draw shape at all) and 1 (draw only the shape; no inversion)
shape_thickness	Thickness of the drawn shape in hundreths of units. Ignored if draw_shape is 0.
passthrough	Allows passing through a portion of the uninverted points; passthrough is the relative density of inverted point to original points, between 0 (result contains only inverted points) and 1 (result contains only original points; no inversion)
guides_enabled	Not used in this version of the variation
color_measure	Measure to use for direct color: 0: none; don’t use direct color 1: distance of destination point from boundary 2: distance of source point from boundary 3: distance between source and destination points 4: distance of destination point from standard circle inversion
color_gradient	How to apply direct color (not used if color_measure is 0) 1: clamp values less than color_low_threshold to the leftmost gradient color and values greater than color_high_threshold to the rightmost gradient color 2: wrap values outside the range color_low_threshold to color_high_threshold to values inside this range; the result is the same as if the gradient was repeated indefinitely to the left and right.
color_low_threshold	Distance value for the leftmost gradient color
color_high_threshold	Distance value for the rightmost gradient color

Special Considerations

There are two anomalies with shape points (when draw_shape ≠ 0) and passthrough points (when passthrough ≠ 0). First, the variation amount is not used so should be set to 1 when these features are enabled. Second, they don’t honor the Preserve Z setting; the workaround is to disable Preserve Z and add zscale to each transform with 2D variations.

Ring mode has some quirks. First, ring_scale must be something other than 1 for it to work, which causes a glitch when ring_mode is 1 and ring_scale is moved gradually to or from 1. Second, it doesn’t work correctly for some values of scale. To ensure proper operation, set ring_scale smaller than 1 when scale ≥ 1 and larger than 1 when scale ≤ 1.