Euclidean is a collection of python utilities for complex numbers,
paths, polygons & Vector3s.
To use euclidean, install python 2.x on your machine, which is
avaliable from http://www.python.org/download/
Then in the folder which euclidean is in, type 'python' in a shell to
run the python interpreter. Finally type 'import euclidean' to import
these utilities and 'from vector3 import Vector3' to import the Vector3
class.
Below are examples of euclidean use.
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calculateAutoRetractDistance(targetPoint,
oozeRate,
feedRateMinute,
zDistanceRatio) |
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addElementToListDictionary(element,
key,
listDictionary)
Add an element to the list table. |
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addElementToListDictionaryIfNotThere(element,
key,
listDictionary)
Add the value to the lists. |
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addElementToPixelList(element,
pixelDictionary,
x,
y)
Add an element to the pixel list. |
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addElementToPixelListFromPoint(element,
pixelDictionary,
point)
Add an element to the pixel list. |
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addHorizontallyBoundedPoint(begin,
center,
end,
horizontalBegin,
horizontalEnd,
path)
Add point if it is within the horizontal bounds. |
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addListToListTable(elementList,
key,
listDictionary)
Add a list to the list table. |
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addLoopToPixelTable(loop,
pixelDictionary,
width)
Add loop to the pixel table. |
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addPathToPixelTable(path,
pixelDictionary,
value,
width)
Add path to the pixel table. |
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addPixelTableToPixelTable(fromPixelTable,
intoPixelTable)
Add from pixel table to the into pixel table. |
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addPixelToPixelTableWithSteepness(isSteep,
pixelDictionary,
value,
x,
y)
Add pixels to the pixel table with steepness. |
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addPointToPath(path,
pixelDictionary,
point,
value,
width)
Add a point to a path and the pixel table. |
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addSegmentToPixelTable(beginComplex,
endComplex,
pixelDictionary,
shortenDistanceBegin,
shortenDistanceEnd,
width)
Add line segment to the pixel table. |
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addSquareTwoToPixelDictionary(pixelDictionary,
point,
value,
width)
Add square with two pixels around the center to pixel dictionary. |
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addSurroundingLoopBeginning(distanceFeedRate,
loop,
z)
Add surrounding loop beginning to gcode output. |
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addToThreadsFromLoop(extrusionHalfWidth,
gcodeType,
loop,
oldOrderedLocation,
nestedRing)
Add to threads from the last location from loop. |
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addToThreadsRemove(extrusionHalfWidth,
nestedRings,
oldOrderedLocation,
threadSequence)
Add to threads from the last location from surrounding loops. |
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addValueSegmentToPixelTable(beginComplex,
endComplex,
pixelDictionary,
value,
width)
Add line segment to the pixel table. |
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addValueToOutput(depth,
keyInput,
output,
value)
Add value to the output. |
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addXIntersectionIndexesFromLoop(frontOverWidth,
loop,
solidIndex,
xIntersectionIndexLists,
width,
yList)
Add the x intersection indexes for a loop. |
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addXIntersectionIndexesFromLoops(frontOverWidth,
loops,
solidIndex,
xIntersectionIndexLists,
width,
yList)
Add the x intersection indexes for a loop. |
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addXIntersectionIndexesFromLoopListsY(loopLists,
xIntersectionIndexList,
y)
Add the x intersection indexes for the loop lists. |
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addXIntersectionIndexesFromLoopsY(loops,
solidIndex,
xIntersectionIndexList,
y)
Add the x intersection indexes for the loops. |
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addXIntersectionIndexesFromLoopY(loop,
solidIndex,
xIntersectionIndexList,
y)
Add the x intersection indexes for a loop. |
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addXIntersectionIndexesFromSegment(index,
segment,
xIntersectionIndexList)
Add the x intersection indexes from the segment. |
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addXIntersectionIndexesFromSegments(index,
segments,
xIntersectionIndexList)
Add the x intersection indexes from the segments. |
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addXIntersectionIndexesFromXIntersections(index,
xIntersectionIndexList,
xIntersections)
Add the x intersection indexes from the XIntersections. |
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addXIntersections(loop,
xIntersections,
y)
Add the x intersections for a loop. |
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addXIntersectionsFromLoopForTable(loop,
xIntersectionsTable,
width)
Add the x intersections for a loop into a table. |
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addXIntersectionsFromLoops(loops,
xIntersections,
y)
Add the x intersections for the loops. |
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addXIntersectionsFromLoopsForTable(loops,
xIntersectionsTable,
width)
Add the x intersections for a loop into a table. |
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compareSegmentLength(endpoint,
otherEndpoint)
Get comparison in order to sort endpoints in ascending order of
segment length. |
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concatenateRemovePath(connectedPaths,
pathIndex,
paths,
pixelDictionary,
segments,
width)
Get connected paths from paths. |
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getAngleAroundZAxisDifference(subtractFromVec3,
subtractVec3)
Get the angle around the Z axis difference between a pair of
Vector3s. |
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getAngleDifferenceByComplex(subtractFromComplex,
subtractComplex)
Get the angle between a pair of normalized complexes. |
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getAreaLoop(loop)
Get the area of a complex polygon. |
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getAreaLoopAbsolute(loop)
Get the absolute area of a complex polygon. |
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getAreaLoops(loops)
Get the area of a list of complex polygons. |
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getAreaRadiusMultiplier(sides)
Get the area radius multiplier for the polygon. |
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getAreaVector3LoopAbsolute(loop)
Get the absolute area of a vector3 polygon. |
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getAroundLoop(begin,
end,
loop)
Get an arc around a loop. |
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getAwayPath(path,
radius)
Get a path with only the points that are far enough away from each
other, except for the last point. |
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getAwayPoints(points,
radius)
Get a path with only the points that are far enough away from each
other. |
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getBackOfLoops(loops)
Get the back of the loops. |
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getBooleanFromDictionary(defaultBoolean,
dictionary,
key)
Get boolean from the dictionary and key. |
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getBooleanFromValue(value)
Get boolean from the word. |
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getBottomByPath(path)
Get the bottom of the path. |
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getBottomByPaths(paths)
Get the bottom of the paths. |
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getClippedAtEndLoopPath(clip,
loopPath)
Get a clipped loop path. |
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getClippedLoopPath(clip,
loopPath)
Get a clipped loop path. |
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getClippedSimplifiedLoopPath(clip,
loopPath,
radius)
Get a clipped and simplified loop path. |
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getComplexByCommaString(valueCommaString)
Get the commaString as a complex. |
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getComplexDefaultByDictionary(defaultComplex,
dictionary,
key)
Get the value as a complex. |
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getComplexDefaultByDictionaryKeys(defaultComplex,
dictionary,
keyX,
keyY)
Get the value as a complex. |
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getComplexByWords(words,
wordIndex=0)
Get the complex by the first two words. |
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getComplexPath(vector3Path)
Get the complex path from the vector3 path. |
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getComplexPathByMultiplier(multiplier,
path)
Get the multiplied complex path. |
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getComplexPaths(vector3Paths)
Get the complex paths from the vector3 paths. |
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getComplexPolygon(center,
radius,
sides,
startAngle=0.0)
Get the complex polygon. |
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getComplexPolygonByComplexRadius(radius,
sides,
startAngle=0.0)
Get the complex polygon. |
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getComplexPolygonByStartEnd(endAngle,
radius,
sides,
startAngle=0.0)
Get the complex polygon by start and end angle. |
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getConcatenatedList(originalLists)
Get the lists as one concatenated list. |
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getConnectedPaths(paths,
pixelDictionary,
width)
Get connected paths from paths. |
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getCrossProduct(firstComplex,
secondComplex)
Get z component cross product of a pair of complexes. |
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getDecimalPlacesCarried(extraDecimalPlaces,
value)
Get decimal places carried by the decimal places of the value plus
the extraDecimalPlaces. |
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getDiagonalFlippedLoop(loop)
Get loop flipped over the dialogonal, in other words with the x and y
swapped. |
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getDiagonalFlippedLoops(loops)
Get loops flipped over the dialogonal, in other words with the x and
y swapped. |
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getDictionaryString(dictionary)
Get the dictionary string. |
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getDistanceToLine(begin,
end,
point)
Get the distance from a vector3 point to an infinite line. |
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getDistanceToLineByPath(begin,
end,
path)
Get the maximum distance from a path to an infinite line. |
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getDistanceToLineByPaths(begin,
end,
paths)
Get the maximum distance from paths to an infinite line. |
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getDistanceToPlaneSegment(segmentBegin,
segmentEnd,
point)
Get the distance squared from a point to the x & y components of
a segment. |
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getDotProduct(firstComplex,
secondComplex)
Get the dot product of a pair of complexes. |
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getDotProductPlusOne(firstComplex,
secondComplex)
Get the dot product plus one of the x and y components of a pair of
Vector3s. |
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getDurationString(seconds)
Get the duration string. |
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getEndpointFromPath(path,
pathIndex)
Get endpoint segment from a path. |
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getEndpointsFromSegments(segments)
Get endpoints from segments. |
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getEndpointsFromSegmentTable(segmentTable)
Get the endpoints from the segment table. |
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getEnumeratorKeys(enumerator,
keys)
Get enumerator keys. |
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getEnumeratorKeysAlwaysList(enumerator,
keys)
Get enumerator keys. |
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getEnumeratorKeysExceptForOneArgument(enumerator,
keys)
Get enumerator keys, except when there is one argument. |
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getFillOfSurroundings(nestedRings,
penultimateFillLoops)
Get extra fill loops of nested rings. |
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getFloatDefaultByDictionary(defaultFloat,
dictionary,
key)
Get the value as a float. |
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getFloatFromValue(value)
Get the value as a float. |
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getFourSignificantFigures(number)
Get number rounded to four significant figures as a string. |
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getFrontOfLoops(loops)
Get the front of the loops. |
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getFrontOverWidthAddXListYList(front,
loopLists,
numberOfLines,
xIntersectionIndexLists,
width,
yList)
Get the front over width and add the x intersection index lists and
ylist. |
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getFrontOverWidthAddYList(front,
numberOfLines,
xIntersectionIndexLists,
width,
yList)
Get the front over width and add the x intersection index lists and
ylist. |
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getHalfSimplifiedLoop(loop,
radius,
remainder)
Get the loop with half of the points inside the channel removed. |
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getHalfSimplifiedPath(path,
radius,
remainder)
Get the path with half of the points inside the channel removed. |
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getHorizontallyBoundedPath(horizontalBegin,
horizontalEnd,
path)
Get horizontally bounded path. |
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getHorizontalSegmentListsFromLoopLists(alreadyFilledArounds,
front,
numberOfLines,
rotatedFillLoops,
width)
Get horizontal segment lists inside loops. |
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getIncrementFromRank(rank)
Get the increment from the rank which is 0 at 1 and increases by
three every power of ten. |
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getInsidesAddToOutsides(loops,
outsides)
Add loops to either the insides or outsides. |
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getIntermediateLocation(alongWay,
begin,
end)
Get the intermediate location between begin and end. |
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getIntersectionOfXIntersectionIndexes(totalSolidSurfaceThickness,
xIntersectionIndexList)
Get x intersections from surrounding layers. |
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getIntersectionOfXIntersectionsTables(xIntersectionsTables)
Get the intersection of the XIntersections tables. |
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getIntFromValue(value)
Get the value as an int. |
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getIsInFilledRegion(loops,
point)
Determine if the point is in the filled region of the loops. |
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getIsInFilledRegionByPaths(loops,
paths)
Determine if the point of any path is in the filled region of the
loops. |
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getIsRadianClose(firstRadian,
secondRadian)
Determine if the firstRadian is close to the secondRadian. |
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getIsWiddershinsByVector3(polygon)
Determine if the polygon goes round in the widdershins direction. |
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getJoinOfXIntersectionIndexes(xIntersectionIndexList)
Get joined x intersections from surrounding layers. |
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getLargestLoop(loops)
Get largest loop from loops. |
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getLeftPoint(points)
Get the leftmost complex point in the points. |
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getLeftPointIndex(points)
Get the index of the leftmost complex point in the points. |
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getListTableElements(listDictionary)
Get all the element in a list table. |
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getLoopCentroid(polygonComplex)
Get the area of a complex polygon using
http://en.wikipedia.org/wiki/Centroid. |
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getLoopConvex(points)
Get convex hull of points using gift wrap algorithm. |
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getLoopConvexCentroid(polygonComplex)
Get centroid of the convex hull of a complex polygon. |
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getLoopInsideContainingLoop(containingLoop,
loops)
Get a loop that is inside the containing loop. |
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getLoopLength(polygon)
Get the length of a polygon perimeter. |
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getLoopStartingNearest(extrusionHalfWidth,
location,
loop)
Add to threads from the last location from loop. |
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getLoopWithoutCloseEnds(close,
loop)
Get loop without close ends. |
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getLoopWithoutCloseSequentialPoints(close,
loop)
Get loop without close sequential points. |
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getMaximum(firstComplex,
secondComplex)
Get a complex with each component the maximum of the respective
components of a pair of complexes. |
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getMaximumByComplexPath(path)
Get a complex with each component the maximum of the respective
components of a complex path. |
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getMaximumByComplexPaths(paths)
Get a complex with each component the maximum of the respective
components of complex paths. |
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getMaximumByVector3Path(path)
Get a vector3 with each component the maximum of the respective
components of a vector3 path. |
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getMaximumByVector3Paths(paths)
Get a complex with each component the maximum of the respective
components of a complex path. |
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getMaximumSpan(loop)
Get the maximum span of the loop. |
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getMinimum(firstComplex,
secondComplex)
Get a complex with each component the minimum of the respective
components of a pair of complexes. |
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getMinimumByComplexPath(path)
Get a complex with each component the minimum of the respective
components of a complex path. |
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getMinimumByComplexPaths(paths)
Get a complex with each component the minimum of the respective
components of complex paths. |
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getMinimumByVector3Path(path)
Get a vector3 with each component the minimum of the respective
components of a vector3 path. |
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getMinimumByVector3Paths(paths)
Get a complex with each component the minimum of the respective
components of a complex path. |
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getNearestDistanceIndex(point,
loop)
Get the distance squared to the nearest segment of the loop and index
of that segment. |
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getNearestPointOnSegment(segmentBegin,
segmentEnd,
point)
Get the nearest point on the segment. |
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getNormalized(complexNumber)
Get the normalized complex. |
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getNormalWeighted(begin,
center,
end)
Get weighted normal. |
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getNumberOfIntersectionsToLeft(loop,
point)
Get the number of intersections through the loop for the line going
left. |
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getNumberOfIntersectionsToLeftOfLoops(loops,
point)
Get the number of intersections through the loop for the line
starting from the left point and going left. |
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getOrderedNestedRings(nestedRings)
Get ordered nestedRings from nestedRings. |
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getPathLength(path)
Get the length of a path ( an open polyline ). |
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getPathsFromEndpoints(endpoints,
maximumConnectionLength,
pixelDictionary,
width)
Get paths from endpoints. |
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getPlaneDot(vec3First,
vec3Second)
Get the dot product of the x and y components of a pair of Vector3s. |
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getPluralString(number,
suffix)
Get the plural string. |
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getPointsByHorizontalDictionary(width,
xIntersectionsDictionary)
Get points from the horizontalXIntersectionsDictionary. |
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getPointsByVerticalDictionary(width,
xIntersectionsDictionary)
Get points from the verticalXIntersectionsDictionary. |
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getRadiusArealizedMultiplier(sides)
Get the radius multiplier for a polygon of equal area. |
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getPointsRoundZAxis(planeAngle,
points)
Get points rotated by the plane angle |
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getPointPlusSegmentWithLength(length,
point,
segment)
Get point plus a segment scaled to a given length. |
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getRandomComplex(begin,
end)
Get random complex. |
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getRank(width)
Get the rank which is 0 at 1 and increases by three every power of
ten. |
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getRotatedComplexes(planeAngle,
points)
Get points rotated by the plane angle |
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getRotatedComplexLists(planeAngle,
pointLists)
Get point lists rotated by the plane angle |
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getRotatedWiddershinsQuarterAroundZAxis(vector3)
Get Vector3 rotated a quarter widdershins turn around Z axis. |
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getRoundedPoint(point)
Get point with each component rounded. |
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getRoundedToPlaces(decimalPlaces,
number)
Get number rounded to a number of decimal places. |
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getRoundedToPlacesString(decimalPlaces,
number)
Get number rounded to a number of decimal places as a string. |
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getRoundedToThreePlaces(number)
Get number rounded to three places as a string. |
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getRoundZAxisByPlaneAngle(planeAngle,
vector3)
Get Vector3 rotated by a plane angle. |
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getSegmentFromPath(path,
pathIndex)
Get endpoint segment from a path. |
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getSegmentFromPoints(begin,
end)
Get endpoint segment from a pair of points. |
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getSegmentsFromXIntersectionIndexes(xIntersectionIndexList,
y)
Get endpoint segments from the x intersection indexes. |
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getSegmentsFromXIntersections(xIntersections,
y)
Get endpoint segments from the x intersections. |
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getSimplifiedLoop(loop,
radius)
Get loop with points inside the channel removed. |
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getSimplifiedLoops(loops,
radius)
Get the simplified loops. |
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getSimplifiedPath(path,
radius)
Get path with points inside the channel removed. |
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getSquareIsOccupied(pixelDictionary,
x,
y)
Determine if a square around the x and y pixel coordinates is
occupied. |
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getSquareLoopWiddershins(beginComplex,
endComplex)
Get a square loop from the beginning to the end and back. |
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getSquareValues(pixelDictionary,
x,
y)
Get a list of the values in a square around the x and y pixel
coordinates. |
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getSquareValuesFromPoint(pixelDictionary,
point)
Get a list of the values in a square around the point. |
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getStepKeyFromPoint(point)
Get step key for the point. |
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getThreeSignificantFigures(number)
Get number rounded to three significant figures as a string. |
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getTopPaths(paths)
Get the top of the paths. |
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getTransferClosestSurroundingLoop(extrusionHalfWidth,
nestedRings,
oldOrderedLocation,
threadSequence)
Get and transfer the closest remaining surrounding loop. |
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getTransferredPaths(insides,
loop)
Get transferred paths from inside paths. |
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getTransferredSurroundingLoops(insides,
loop)
Get transferred paths from inside surrounding loops. |
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getTranslatedComplexPath(path,
translateComplex)
Get the translated complex path. |
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getVector3Path(complexPath,
z=0.0)
Get the vector3 path from the complex path. |
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getVector3Paths(complexPaths,
z=0.0)
Get the vector3 paths from the complex paths. |
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getWiddershinsUnitPolar(angle)
Get polar complex from counterclockwise angle from 1, 0. |
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getXIntersectionIfExists(beginComplex,
endComplex,
y)
Get the x intersection if it exists. |
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getXIntersectionsFromIntersections(xIntersectionIndexList)
Get x intersections from the x intersection index list, in other
words subtract non negative intersections from negatives. |
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getXYComplexFromVector3(vector3)
Get an xy complex from a vector3 if it exists, otherwise return None. |
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getYIntersectionIfExists(beginComplex,
endComplex,
x)
Get the y intersection if it exists. |
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getZComponentCrossProduct(vec3First,
vec3Second)
Get z component cross product of a pair of Vector3s. |
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isInsideOtherLoops(loopIndex,
loops)
Determine if a loop in a list is inside another loop in that list. |
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isLineIntersectingInsideXSegment(beginComplex,
endComplex,
segmentFirstX,
segmentSecondX,
y)
Determine if the line is crossing inside the x segment. |
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isLineIntersectingLoop(loop,
pointBegin,
pointEnd)
Determine if the line is intersecting loops. |
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isLineIntersectingLoops(loops,
pointBegin,
pointEnd)
Determine if the line is intersecting loops. |
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isLoopIntersectingInsideXSegment(loop,
segmentFirstX,
segmentSecondX,
segmentYMirror,
y)
Determine if the loop is intersecting inside the x segment. |
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isLoopIntersectingLoop(loop,
otherLoop)
Determine if the loop is intersecting the other loop. |
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isLoopIntersectingLoops(loop,
otherLoops)
Determine if the loop is intersecting other loops. |
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isLoopListIntersectingInsideXSegment(loopList,
segmentFirstX,
segmentSecondX,
segmentYMirror,
y)
Determine if the loop list is crossing inside the x segment. |
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isLoopListIntersecting(loops)
Determine if a loop in the list is intersecting the other loops. |
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isPathEntirelyInsideLoop(loop,
path)
Determine if a path is entirely inside another loop. |
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isPathEntirelyInsideLoops(loops,
path)
Determine if a path is entirely inside another loop in a list. |
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getEnclosingLoops(loops,
path)
Returns loops within which the path is entirely contained. |
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getClosestEnclosingLoop(loops,
path)
Returns closest loop within which the path is entirely contained. |
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isPathInsideLoop(loop,
path)
Determine if a path is inside another loop. |
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isPathInsideLoops(loops,
path)
Determine if a path is inside another loop in a list. |
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isPixelTableIntersecting(bigTable,
littleTable,
maskTable={ } )
Add path to the pixel table. |
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isPointInsideLoop(loop,
point)
Determine if a point is inside another loop. |
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isSegmentCompletelyInX(segment,
xFirst,
xSecond)
Determine if the segment overlaps within x. |
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isWiddershins(polygonComplex)
Determine if the complex polygon goes round in the widdershins
direction. |
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isWithinChannel(channelRadius,
pointIndex,
loop)
Determine if the the point is within the channel between two adjacent
points. |
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isXSegmentIntersectingPath(path,
segmentFirstX,
segmentSecondX,
segmentYMirror,
y)
Determine if a path is crossing inside the x segment. |
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isXSegmentIntersectingPaths(paths,
segmentFirstX,
segmentSecondX,
segmentYMirror,
y)
Determine if a path list is crossing inside the x segment. |
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joinSegmentTables(fromTable,
intoTable)
Join both segment tables and put the join into the intoTable. |
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joinXIntersectionsTables(fromTable,
intoTable)
Join both XIntersections tables and put the join into the intoTable. |
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overwriteDictionary(fromDictionary,
keys,
toDictionary)
Overwrite the dictionary. |
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removeElementFromDictionary(dictionary,
key)
Remove element from the dictionary. |
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removeElementFromListTable(element,
key,
listDictionary)
Remove an element from the list table. |
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removeElementFromPixelListFromPoint(element,
pixelDictionary,
point)
Remove an element from the pixel list. |
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removeElementsFromDictionary(dictionary,
keys)
Remove list from the dictionary. |
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removePrefixFromDictionary(dictionary,
prefix)
Remove the attributes starting with the prefix from the dictionary. |
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removePixelTableFromPixelTable(pixelDictionaryToBeRemoved,
pixelDictionaryToBeRemovedFrom)
Remove pixel from the pixel table. |
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removeTrueFromDictionary(dictionary,
key)
Remove key from the dictionary in the value is true. |
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removeTrueListFromDictionary(dictionary,
keys)
Remove list from the dictionary in the value is true. |
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subtractXIntersectionsTable(subtractFromTable,
subtractTable)
Subtract the subtractTable from the subtractFromTable. |
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swapList(elements,
indexBegin,
indexEnd)
Swap the list elements. |
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toggleHashtable(hashtable,
key,
value)
Toggle a hashtable between having and not having a key. |
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transferClosestFillLoop(extrusionHalfWidth,
oldOrderedLocation,
remainingFillLoops,
nestedRing)
Transfer the closest remaining fill loop. |
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transferClosestPath(oldOrderedLocation,
remainingPaths,
nestedRing)
Transfer the closest remaining path. |
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transferClosestPaths(oldOrderedLocation,
remainingPaths,
nestedRing)
Transfer the closest remaining paths. |
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transferPathsToSurroundingLoops(nestedRings,
paths)
Transfer paths to surrounding loops. |
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translateVector3Path(path,
translateVector3)
Translate the vector3 path. |
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translateVector3Paths(paths,
translateVector3)
Translate the vector3 paths. |
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unbuckleBasis(basis,
maximumUnbuckling,
normal)
Unbuckle space. |
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getFlattenedNestedRings(nestedRings)
Get flattened nested rings. |
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