ATAVUSIA JOURNAL OF DESIGN
NESTING
FORMULATIONS
VISUAL GEOMETRIES AND TRANSFORMATIONS PRODUCED WITH TRANSFORM BRUSHES
Polygons, circles, ellipses
Dissections, bisections, diagonals, medians, perpendiculars, diameters, radius
Inscribed and circumscribed
Stellated
stellated regular polygons, extensions, compound, complex, polytope, rhomboid, kite,
compression, graphic star forms, convex curved, concave curved, wide angle. Stars in circular,
square, elliptic and oval formations, and formations on columns, in arcs, and in envelopes.
Dilations
dilations, similarity dilations
Polyhedra, 2D Solids, Orthographic Brushes
cylinders, prisms, biprisms, triprisms, pyramids, bipyramids, sloped face, frustums, intersecting
planes, intersections, hyperspace, tetrahedron, cube, octahedron, dodecahedron, icosahedron,
cuboctahedron, truncated square trapezohedron, truncated square pyramid, pentakis
icosidodecahedron
Projection
Inverse transformations
Compound and composite transformations
Envelopes
Envelopes of ellipses, envelopes of squares, astroids,
envelope of pencils, conic envelope, torus, shaping envelopes
Graph theory diagrams
regular, cyclic, wheel, star, fano plane, sun, octahedral, gem, zonohedron, complete,
cubical, prism, bicubic, Mobius-Kantor, hypercube, tetrahedral, genus 0, 1, 2, & 4
Special curves
involute, reuleaux, rosette, roulette, lemniscate, limacon, lobed, cardioid,
epicycloidal, hypocycloid, cycloid, epitrochoid, great circle ellipses,
rosetta orbit curves, hypotrochoid, nephroid, helix, parabolic, hyperbolic
Spirals
Archimedean, cycloids and wave forms in Archimedean spirals, equiangular, logarithmic, Doyle,
Fermat, hyperbolic, parabolic, gnomic, Baravelle, equiangular spiraling dilations, spiraling
similarities, angle spirals, dynamic symmetry spirals, elliptical, conic, growth, radial, whirlpool,
spiraled polygons, spiraled circles and ellipses, 180 degree congruence transform spirals, spiraled
geometric extensions, spiraling special curves, spiraled tilings, page spirals, plus spiraling
designs, foliage, patterns, lines, and line shapes
Rings and formations
cohesive rings of ellipses, polygons, special curves, shapes, designs, patterns,
line shape rings, annulus, circle packing rings, Doyle spirals, polygonal
proportionate reduction rings. Polygons, circles,
shapes and multiples in formations.
3 CONGRUENT CIRCLES
transform brush
solution
Proportion, ratios, and other wonders
phi, precise circumscribe any quadrilateral,
pi, and area brushes, ratio formulations,
palindromic numbers, nesting numbers
Tiling and tessellations
isohedral, homeomeric, isotoxal, isogonal,
monohedral, regular polygon tilings,
star polygon tilings, as well as, prototiles
Lattices
square, hexagonal, triangular
Polyforms
monomino, domino, triomino, tetromino, pentomino, polyiamond
Packing and covering
Strip tiling
Coordinate space example brushes
sets, formations, position, spacing, cutting, scaling, reflection, translation, rotation
Classic geometry brushes
Babylonian Pi, Archimedes Pi, Pythagorean tiling, Lute of Pythagoras, ancient Egyptian geometry of
the Rhind Papyrus quadrature of the circle, Hippocrates of Chios Lune, Euclid’s proposition 16,
Tetracys, finding a single-click transform brush solution for the 3 congruent circles problem
suggested in Proofs Without Words III.
5
Rotation transforms, page protractor,
isometric & diamond grid brushes
360
rotation
positions
(degrees)
in
two
brushes,
sets
of
special
rotations,
including
fractional
rotations,
rotations
for
graphic
design,
rotation
transforms
which
produce
cuts
and
sections.
Master
brushes
for
building
a
page
protractor.
Square,
diamond,
and
isometric grid brushes
PAGE PROTRACTOR
a useful background layer for
verifying angle of rotation
UNIQUE TILING BRUSHES
INTERSECTION OF 3 TRUNCATED
DODECAGONAL PYRAMIDS
Parabolic
Curve
Cycloids in an
equiangular
spiral
Polygon and circle rings in a hexagonal lattice form
Symmetry 5 crystal brush
astroid
Fano Plane
Multiple Tetrahedrons in formation
Copyright 2023, All Rights Reserved. J. L. Morrison. This includes all illustrations and written material
DILATIONS
The
geometric
design,
left,
was
created
in
a
total
of
6
seconds,
with
three
single-click
brushes.
The
original
drawing
size
is
4000
x
4000
pixels
with
a
resolution
of
300
dpi.
Transform
brushes
are
not
producing
clones
or
vectorized
copies
of
images.
Color
fill
was
added to this image.
Each
transform
brush
produces
its
image
according
to
it’s
brush
build.
The
brushes
are
built
with
Euclidean
and
affine
transforms
formulated
through
the
computer
language
embedded in the program’s brush effects.
