For this week we\u2019ll start into the powerful world of symmetry and reflections. ShapeJS allows arbitrary transformations of objects and as we\u2019ll see in this post this has great power and some sharp edges to avoid. Guest writing this week is Vladimir Bulatov, he\u2019s the math whiz behind the curtains of ShapeJS.<\/p>\n
PeriodicWrap<\/b> is a ShapeJS transformation which is most useful for creating repeated shapes and patterns. However if used incorrectly it can produce unexpected results. The purpose of this tutorial is to provide basic info and examples with correct use of PeriodicWrap, highlight potential problems and suggest possible solutions.<\/p>\n
PeriodicWrap generates a fill of the three dimensional space (tiling) with copies of a single tile – the fundamental domain. PeriodicWrap is defined by linearly independent basis vectors and an origin. All parameters have type Vector3d. Basis vectors define the shape and orientation of the fundamental domain and the origin defines the place of the fundamental domain in space. There are 3 variants of PeriodicWrap one-, two- and three-periodic. This week we\u2019ll examine the one periodic version, and in a later post we\u2019ll cover the more complex versions. <\/p>\n
One-periodic wrap<\/Strong>
\nWe start with the simplest variant – one-periodic. It is defined by one basis vector and origin. The origin has default value (0,0,0) which means the PeriodicWrap is located at the origin of the coordinate axes.<\/p>\n