Copy Tools Ipelet

This Ipelet implements 3 tools to create different types of patterns in Ipe:

Linear patterns

Demo

Usage

• Select objects to be copied (all types are allowed, including nested groups of objects)
• Select Ipelets->Copy Tools->Linear/Grid Pattern
• Move the two endpoints of the "displacement vector"
• Specify the number of instances:
  • use number keys 0-9 or
  • use j or k to increment or decrement the number or
  • input the exact number by right clicking and selecting "Set number of total instances"
• To apply the pattern press space or right right click and select "Accept"

Circular pattern

Demo

Usage

• Select objects to be copied (all types are allowed, including nested groups of objects)
• Set the origin of the current axis system (see Ipe manual)
• Select Ipelets->Copy Tools->Circular Pattern
• Specify the number of instances:
  • use number keys 0-9 or
  • use j or k to increment or decrement the number or
  • input the exact number by right clicking and selecting "Set number of total instances"
• If desired, the current axis system can be reset at any time (see video)
• The instances can either be distributed automatically over 360° or a fixed angle can be set between the instances by right clicking and selecting "Set fixed angle between instances"
• To apply the pattern press space or right right click and select "Accept"

Patterns along paths

Demo: Distribute along Path

Demo: Copy along Path with fixed distances

Usage

• Select objects to be copied (all types are allowed, including nested groups of objects)
• Select path along which you want to copy as primary selection (last selection made). Any contiguous path consisting of a combination of line segments, circular arcs or different types of splines is allowed.
• Select Ipelets->Copy Tools->Pattern along Path
• Specify the number of instances:
  • use number keys 0-9 or
  • use j or k to increment or decrement the number or
  • input the exact number by right clicking and selecting "Set number of total instances"
• If desired, the orientation of the instances can either be fixed or it can be aligned with the tangent of the path by selection in the context menu
• The instances can either be distributed automatically along the path or a fixed distance can be set between the instances by right clicking and selecting "Set fixed distance between instances"
• To apply the pattern press space or right right click and select "Accept"

Installation

Copy copytools.lua to a location found by IPE.

(Normally this is ~/.ipe/ipelets for Linux and %userprofile%\ipelets for Windows (see Help->Show configuration))

Technical Details & Lessons Learned

• The implementation of linear and circular patterns was relatively straight forward
• For patterns along a path, each type of subpath (line segment, spline, circular arcs) has to be treated differently
• Since there is no closed form solution for the arc length of a Bezier spline, the arc length of each Bezier subpath has been computed with a lookup table
• The computed LUTs have also been used to place the objects at specific waypoints by interpolating between LUT entries (see https://pomax.github.io/bezierinfo/#tracing)
• The arc length of a circle can easily be calculated. For the arc length of an ellipse, however, an elliptic integral must be solved. Since it is also extremely difficult to get from a non-uniformly transformed circular arc to the ellipse equation in Ipe, all circular arcs were simply approximated as splines in a preprocessing step (see https://pomax.github.io/bezierinfo/#circles_cubic). For this purpose, the circular arc was transformed into the unit circle by using its inverse (nested) transformation matrix, approximated as a spline and transformed back again.
• The tangent of a waypoint is very easy to calculate. It is used for the orientation of the copied instances.

Synergies with my lassotool:

• For nested groups of objects, the transformation matrices have to be applied recursively
• The outline of an image object is not directly accessible. One option is to apply the inverse transformation matrix, get the bounding box and again apply the forward transformation.
• The outline of a text object is not directly accessible. One option is to calculate the outline based on the position, dimensions, alignment and transformation matrix