mirror of https://CODE.RHODECODE.COM/u/O/O/O
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
533 lines
16 KiB
533 lines
16 KiB
<?xml version="1.0" encoding="utf-8" standalone="yes"?>
|
|
<Fractal BackgroundVisible="True" BackColor="FFFFFF00" BorderWidth="0" StripBorder="True" PixelSize="0.00548779710473845" Pixels.X="729" Pixels.Y="729" ClassicProcessing="None" OrbitTrapProcessing="ActivateControllers" ClassicMaxDwell="1" CycleDetectionActive="False" SolidGuessing="None">
|
|
<FractalNotes><![CDATA[]]></FractalNotes>
|
|
<FractalEquation Id="adb85431-618d-491f-b8c5-08555b119814" Title="Pixel" MaxPower="1">
|
|
<Instructions><![CDATA[
|
|
comment:
|
|
|
|
This equation can be used when no equation is necessary.
|
|
By setting the MinDwell/MaxDwell to 1 below, we limit
|
|
the iteration to a single step for best performance.
|
|
|
|
global:
|
|
|
|
FSK.OverrideValue("MinDwell", 1)
|
|
FSK.OverrideValue("MaxDwell", 1)
|
|
|
|
iterate:
|
|
|
|
z = c
|
|
]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</FractalEquation>
|
|
<TransformationArray>
|
|
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</Transformation>
|
|
</TransformationArray>
|
|
<TransformationArray>
|
|
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</Transformation>
|
|
</TransformationArray>
|
|
<AlternateValueInfo />
|
|
<AlternateValueInfo />
|
|
<OrbitTrapInfo TrapValueNTrapPreProcessing="CenterReflect" TrapValueNTrapStyle="Flat" TrapValueNSmoothing="Linear" TrapValueNTrapPreProcessing1="CenterReflect" TrapValueNTrapStyle1="Flat" TrapValueNSmoothing1="Linear" TrapValueNTrapPreProcessing2="CenterReflect" TrapValueNTrapStyle2="Flat" TrapValueNSmoothing2="Linear" TrapValueNTrapPreProcessing3="CenterReflect" TrapValueNTrapStyle3="Flat" TrapValueNSmoothing3="Linear">
|
|
<OrbitTrapArray TrapIndexMapping="CombinedIndex" TrapDeltaMapping="TrapDelta" BlendValues="False">
|
|
<OrbitTransform />
|
|
<OrbitTransform />
|
|
<TransformationArray>
|
|
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</Transformation>
|
|
</TransformationArray>
|
|
<TransformationArray>
|
|
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</Transformation>
|
|
</TransformationArray>
|
|
<SymmetryTransformation Id="8301dc6c-2273-4fb9-ada8-2ded2833031f" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</SymmetryTransformation>
|
|
<OrbitTrapItem>
|
|
<OrbitTrap Id="4e4b2e73-dc52-4107-bb98-f9abb8745748" Title="Unit Circle Group">
|
|
<Instructions><![CDATA[
|
|
comment:
|
|
|
|
trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring)
|
|
trappedPoint.Delta is the level: 0 - Steps-1
|
|
|
|
See the paper:
|
|
"Evolution of Math into Art via Mobius Transformations"
|
|
by Anne M. Burns, Department of Mathematics,
|
|
Long Island University.
|
|
http://myweb.cwpost.liu.edu/aburns/
|
|
|
|
Also, see pages 88-89 in the book:
|
|
"Indra's Pearls, The Vision of Felix Klein"
|
|
by David Mumford, Caroline Series, David Wright.
|
|
http://klein.math.okstate.edu/IndrasPearls/
|
|
|
|
global:
|
|
|
|
Complex ShowCenter[] = LC1,LC2,LC3,LC4,LC5,LC6,LC7,LC8,LC9,LC10,LC11,LC12,LC13,LC14,LC15,LC16
|
|
Complex ShowRing[] = LR1,LR2,LR3,LR4,LR5,LR6,LR7,LR8,LR9,LR10,LR11,LR12,LR13,LR14,LR15,LR16
|
|
AbsV = Sqrt(AbsU^2 - 1)
|
|
u = AbsU * Cis(DegreeToRadian(ArgU))
|
|
v = AbsV * Cis(DegreeToRadian(ArgV))
|
|
Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u))
|
|
Mobius m[N+1]
|
|
'
|
|
' Given N, find radius R such that N circles with radius R can be
|
|
' placed along the inside of the unit circle, each tangent to the
|
|
' unit circle and each of its two adjacent neighbors. The centers
|
|
' of all circles are a distance of 1-R from the origin. The centers
|
|
' of all circles form a regular polygon P with N sides and each edge
|
|
' has length = 2*(1-R)*Sin(pi/N). Since all N circles are pairwise
|
|
' tangent, the edge of P must equal 2*R, so 2*R = 2*(1-R)*Sin(pi/N).
|
|
' Solving for R yields R = 1/(1+1/Sin(pi/N)).
|
|
'
|
|
r = 1/(1+1/Sin(Math.PI/N))
|
|
|
|
step = 2*Math.PI/N
|
|
ang = IIf(Shift, step/2, 0)
|
|
'
|
|
' Generate the Mobius transformation that transforms the
|
|
' unit circle into the circle in the center of the ring.
|
|
'
|
|
m[0] = Mobius(1-2*r, 0, 0, 1)
|
|
'
|
|
' Generate the set of N Mobius transformations the
|
|
' transform the unit circle into the i'th circle in the
|
|
' ring, where i = 1 to N.
|
|
'
|
|
for (i = 1, i <= N, i += 1) {
|
|
rotate = Cis(ang)
|
|
|
|
m[i] = Mobius.Multiply( \
|
|
Mobius(r*rotate, (1-r)*rotate, 0, 1), \
|
|
UnitCircleGroup \
|
|
)
|
|
ang += step
|
|
}
|
|
'
|
|
' Assign Total = the total number of circles.
|
|
'
|
|
const Complex Total = 0
|
|
count = N+1
|
|
|
|
for (i = 0, i < Steps, i += 1) {
|
|
Total += count
|
|
count *= N+1
|
|
}
|
|
const Circle c[Total]
|
|
const Complex index[Total]
|
|
const Complex level[Total]
|
|
Circle UnitCircle = CircleC(0, 1)
|
|
'
|
|
' Generate the base ring and center circles.
|
|
'
|
|
for (i = 0, i <= N, i += 1) {
|
|
c[i] = Mobius.TransformCircle(m[i], UnitCircle)
|
|
index[i] = i
|
|
level[i] = 0
|
|
}
|
|
count = N+1
|
|
max = 0
|
|
'
|
|
' Generate the remaining circles.
|
|
'
|
|
if (Steps > 1) {
|
|
for (i = 1, i < Steps, i += 1) {
|
|
min = max
|
|
max = count
|
|
|
|
for (j = min, j < max, j += 1) {
|
|
for (k = 0, k < N+1, k += 1) {
|
|
c[count] = Mobius.TransformCircle(m[k], c[j])
|
|
'
|
|
' Skip circles that are too small.
|
|
'
|
|
if (c[count].Radius >= RadiusMin) {
|
|
index[count] = index[j]
|
|
level[count] = i
|
|
count += 1
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
'
|
|
' Reset Total in case you skipped circles that were too small.
|
|
'
|
|
Total = count
|
|
|
|
CurveTrap.Initialize( \
|
|
Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \
|
|
)
|
|
'
|
|
' Add the circles to the trap based on user criteria.
|
|
'
|
|
for (i = 0, i < Total, i += 1) {
|
|
lev = level[i]
|
|
idx = index[i]
|
|
'
|
|
' Note: idx=N for center circles.
|
|
'
|
|
if (idx = 0) {
|
|
if (ShowCenter[lev]) {
|
|
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev)
|
|
}
|
|
} else {
|
|
if (ShowRing[lev]) {
|
|
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev)
|
|
}
|
|
}
|
|
}
|
|
|
|
trap:
|
|
|
|
trappedPoint = CurveTrap.Apply(z)
|
|
|
|
properties:
|
|
|
|
divider {
|
|
caption = "General Options"
|
|
}
|
|
option Center {
|
|
type = Complex
|
|
caption = "Center"
|
|
details = "Center of trap"
|
|
default = 0
|
|
}
|
|
option Angle {
|
|
type = Float
|
|
caption = "Angle"
|
|
details = "Angle of rotation"
|
|
default = 0
|
|
range = [-360,360]
|
|
}
|
|
option Scale {
|
|
type = Float
|
|
caption = "Scale"
|
|
details = "Scale factor applied to trap"
|
|
range = (0,)
|
|
default = 2
|
|
}
|
|
option Solid {
|
|
type = Boolean
|
|
caption = "Solid"
|
|
details = "Check to create solid trap"
|
|
default = False
|
|
}
|
|
option AlternateAngle {
|
|
type = Boolean
|
|
caption = "Alternate Angle"
|
|
details = "Use alternate angle calculation"
|
|
default = False
|
|
}
|
|
option LineWidth {
|
|
type = Float
|
|
caption = "Line Width"
|
|
details = "Extent of trap on either side of curve (> 0)"
|
|
range = (0,)
|
|
default = 0.00411522633744855967078189300413
|
|
enabled = ~Solid
|
|
}
|
|
divider {
|
|
caption = "U/V Controls"
|
|
}
|
|
option AbsU {
|
|
type = Float
|
|
caption = "Abs(U)"
|
|
details = "Magnitude of U (1-2)"
|
|
default = 1.1
|
|
range = [1,2]
|
|
}
|
|
option ArgU {
|
|
type = Float
|
|
caption = "Arg(U)"
|
|
details = "Angle of U"
|
|
default = 0
|
|
range = [-360,360]
|
|
}
|
|
option ArgV {
|
|
type = Float
|
|
caption = "Arg(V)"
|
|
details = "Angle of V"
|
|
default = 180
|
|
range = [-360,360]
|
|
}
|
|
divider {
|
|
caption = "Circle Controls"
|
|
}
|
|
option N {
|
|
type = IntegerEnum(3,12)
|
|
caption = "N"
|
|
details = "Number of base circles"
|
|
default = 4
|
|
}
|
|
option Steps {
|
|
type = IntegerEnum(1,16)
|
|
caption = "Steps"
|
|
details = "Number of inversion steps"
|
|
default = 7
|
|
}
|
|
option Shift {
|
|
type = Boolean
|
|
caption = "Shift"
|
|
details = "Check to rotate initial chain by pi/N"
|
|
default = False
|
|
}
|
|
option RadiusMin {
|
|
type = Float
|
|
caption = "Radius Min"
|
|
details = "Minimum acceptable circle radius"
|
|
default = 0
|
|
range = [0,)
|
|
}
|
|
#define ShowLevel(Index)
|
|
|
|
divider {
|
|
caption = "Level #Index# Options"
|
|
}
|
|
option LR#Index# {
|
|
type = Boolean
|
|
caption = "Show Ring"
|
|
details = "Show ring of circles at level #Index#"
|
|
default = True
|
|
enabled = Steps >= #Index#
|
|
}
|
|
option LC#Index# {
|
|
type = Boolean
|
|
caption = "Show Center"
|
|
details = "Show center circle at level #Index#"
|
|
default = True
|
|
enabled = Steps >= #Index#
|
|
}
|
|
#end
|
|
|
|
#include ShowLevel("1")
|
|
#include ShowLevel("2")
|
|
#include ShowLevel("3")
|
|
#include ShowLevel("4")
|
|
#include ShowLevel("5")
|
|
#include ShowLevel("6")
|
|
#include ShowLevel("7")
|
|
#include ShowLevel("8")
|
|
#include ShowLevel("9")
|
|
#include ShowLevel("10")
|
|
#include ShowLevel("11")
|
|
#include ShowLevel("12")
|
|
#include ShowLevel("13")
|
|
#include ShowLevel("14")
|
|
#include ShowLevel("15")
|
|
#include ShowLevel("16")]]></Instructions>
|
|
<PropertyValueOverrides>
|
|
<Option Name="Solid" Type="BooleanOption" Value="True" />
|
|
<Option Name="LineWidth" Type="FloatOption" Value="0.00411522633744855" />
|
|
<Option Name="ArgU" Type="FloatOption" Value="180" />
|
|
<Option Name="ArgV" Type="FloatOption" Value="0" />
|
|
<Option Name="Steps" Type="IntegerEnumOption" Value="7" />
|
|
<Option Name="LR1" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR2" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR3" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR4" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR5" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR6" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR7" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR8" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR9" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR10" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR11" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR12" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR13" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR14" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR15" Type="BooleanOption" Value="False" />
|
|
<Option Name="LR16" Type="BooleanOption" Value="False" />
|
|
</PropertyValueOverrides>
|
|
</OrbitTrap>
|
|
</OrbitTrapItem>
|
|
</OrbitTrapArray>
|
|
<OrbitTrapMasterController Id="02699986-4214-4098-b68b-48285874bc4e" Title="⠀">
|
|
<Instructions><![CDATA[
|
|
comment:
|
|
|
|
Return color computed by 1st controller.
|
|
|
|
color:
|
|
|
|
color = Controller.Color(0)
|
|
]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</OrbitTrapMasterController>
|
|
<OrbitTrapControllerArray>
|
|
<OrbitTrapController Id="29fbd0db-b470-4d0d-ad93-e4d5d937ef86" Title="ⵔ·ⵔ" ApplyDepth="False" Apply3D="False">
|
|
<GradientArray />
|
|
<TextureArray />
|
|
<Instructions><![CDATA[
|
|
comment:
|
|
|
|
This controller colors each trap based on the
|
|
property 'Index Map' and the point's 'Trap Dwell'
|
|
'Trap Index' or 'Trap Delta'. You can define up to
|
|
16 colors and these are mapped to the index map
|
|
values. Offset can be used to shift the set of
|
|
colors with respect to value 0.
|
|
|
|
If Cutouts are active, the trap is divided into
|
|
N sectors and a user defined percent of each
|
|
sector is inverted with respect to the 3D shading
|
|
effect. This gives the appearance that part of
|
|
the trap surface has been cutout or folded over.
|
|
|
|
The Cutout effect only looks good if the trap
|
|
is a solid shape. For example, the 'Shape',
|
|
'Tangent Circles', 'Shapes' and 'Squares'
|
|
traps support a 'Solid' property that is used to
|
|
produce a solid figure. You should check this
|
|
property to display Cutouts.
|
|
|
|
Also note that the Cutout effect only works if
|
|
the trap's angle is given relative to the center
|
|
of the solid shape. This is always the case when
|
|
the trap is composed of a single shape. However,
|
|
when the trap is composed of several shapes arranged
|
|
in a pattern like the 'Tangent Circles', 'Shapes' and
|
|
'Squares' traps, the angle is given relative to the
|
|
center of the pattern not the individual shapes.
|
|
In those cases, you will need to check the
|
|
'Alternate Angle' property on the properties page
|
|
for the specific trap so the angle is given relative
|
|
to the individual shapes.
|
|
|
|
global:
|
|
|
|
const Complex angleShift = SectorAngle / 360
|
|
const Complex percentSolid = 1 - PercentCutout
|
|
|
|
color:
|
|
|
|
switch (IndexMap) {
|
|
case IndexMapTypes.TrapDwell: index = Sample.TrapDwellRaw
|
|
case IndexMapTypes.TrapIndex: index = Sample.TrapIndexRaw
|
|
case IndexMapTypes.TrapDelta: index = Sample.TrapDeltaRaw
|
|
case IndexMapTypes.Alternate1Index: index = Sample.Alternate1IndexRaw
|
|
}
|
|
color = Colors[WrapIndex(Offset + index, Count)]
|
|
|
|
if (ApplyCutouts) {
|
|
r = Sectors * Wrap(Sample.TrapAngle - angleShift)
|
|
r = r - Int(r)
|
|
v = Abs(Sample.TrapValue)
|
|
|
|
compositeHeight = IIf(r < percentSolid, v, Blend(0.75, 0.25, v))
|
|
} else {
|
|
compositeHeight = Sample.TrapValue
|
|
}
|
|
|
|
properties:
|
|
|
|
divider {
|
|
caption = "Index Map"
|
|
}
|
|
enum IndexMapTypes {
|
|
TrapDwell, "Trap Dwell"
|
|
TrapIndex, "Trap Index"
|
|
TrapDelta, "Trap Delta"
|
|
Alternate1Index , "Alternate 1 Index"
|
|
}
|
|
option IndexMap {
|
|
type = IndexMapTypes
|
|
caption = "Index Map"
|
|
details = "Color index map"
|
|
default = IndexMapTypes.TrapDwell
|
|
}
|
|
divider {
|
|
caption = "Color Map"
|
|
}
|
|
option Count {
|
|
type = IntegerEnum(1,32)
|
|
caption = "Count"
|
|
details = "Number of colors to use"
|
|
default = 8
|
|
}
|
|
option Colors {
|
|
type = ColorSet[Count]
|
|
caption = "Colors"
|
|
default = FF00AE, FF2020, FF8200, FFFF00, 00FF6C, 00FFFF, 4040FF, AE60FF
|
|
}
|
|
option Offset {
|
|
type = IntegerEnum(0,31)
|
|
caption = "Offset"
|
|
details = "Offset into set of colors"
|
|
default = 0
|
|
}
|
|
divider {
|
|
caption = "Cutouts (Solid traps only)"
|
|
}
|
|
option ApplyCutouts {
|
|
type = Boolean
|
|
caption = "Active"
|
|
details = "Activate cutout effects"
|
|
default = False
|
|
}
|
|
option Sectors {
|
|
type = IntegerEnum(2,16)
|
|
caption = "Sectors"
|
|
details = "Number of sectors"
|
|
default = 2
|
|
enabled = ApplyCutouts
|
|
}
|
|
option SectorAngle {
|
|
type = Float
|
|
caption = "Angle"
|
|
details = "Starting angle of 1st sector"
|
|
default = 0
|
|
range = [-360,360]
|
|
enabled = ApplyCutouts
|
|
}
|
|
option PercentCutout {
|
|
type = Float
|
|
caption = "Percent Cutout"
|
|
details = "Percent of sector that is cutout"
|
|
range = [0,1]
|
|
default = 0.5
|
|
enabled = ApplyCutouts
|
|
}
|
|
]]></Instructions>
|
|
<PropertyValueOverrides>
|
|
<Option Name="IndexMap" Type="EnumOption" Value="IndexMapTypes.TrapDelta" />
|
|
<Option Name="Count" Type="IntegerEnumOption" Value="10" />
|
|
<Option Name="Colors" Type="ColorSetOption" Value="A9A9A9,B2B2B2,BABABA,C3C3C3,CBCBCB,D4D4D4,DCDCDC,E5E5E5,EDEDED,F6F6F6" />
|
|
</PropertyValueOverrides>
|
|
</OrbitTrapController>
|
|
</OrbitTrapControllerArray>
|
|
<SampleDataNormalizer>
|
|
<NormalizerDescriptor />
|
|
</SampleDataNormalizer>
|
|
<SampleDataNormalizer>
|
|
<NormalizerDescriptor />
|
|
</SampleDataNormalizer>
|
|
<SampleDataNormalizer>
|
|
<NormalizerDescriptor />
|
|
</SampleDataNormalizer>
|
|
</OrbitTrapInfo>
|
|
<TransformationArray>
|
|
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity">
|
|
<Instructions><![CDATA[]]></Instructions>
|
|
<PropertyValueOverrides />
|
|
</Transformation>
|
|
</TransformationArray>
|
|
<TriangleMetricSet>
|
|
<Instructions><![CDATA[metric = p1]]></Instructions>
|
|
<TriangleMetric />
|
|
<TriangleMetric />
|
|
<TriangleMetric />
|
|
</TriangleMetricSet>
|
|
</Fractal>
|