def boundarycompute(self): try: return self.boundary except: if self[0].str2[6:9] != 'GLY': atoms = self.findatoms([" N "," C "," CA "," O "," OT1", " CB "]) else: atoms = self.findatoms([" N "," C "," CA "," O "," OT1", " HA2"]) atoms.remove(0) posterm = vector.Nlocation(atoms[1].coords(),atoms[2].coords(),atoms[3].coords()) axis = vector.translate(vector.minus(atoms[0].coords()))(posterm) N1 = vector.unit(axis) length = vector.norm(axis) N2 = vector.unit(vector.translate(vector.minus(atoms[2].coords()))(atoms[4].coords())) self.boundary = [atoms[0].coords(), N1, N2, length] return self.boundary
def circleArcAroundPivot(pivot, start, end): pivotToStart = vector.translate(vector.minus(pivot))(start) pivotToEnd = vector.translate(vector.minus(pivot))(end) normalToPlane = vector.crossproduct(pivotToStart,pivotToEnd) firstRadialDirection = vector.crossproduct(normalToPlane, pivotToStart) planeCoefficients = pivotToEnd def dotByPlaneCoefficients(vec): output = 0 for i in range(0,3): output += planeCoefficients[i] * vec[i] return output t = (dotByPlaneCoefficients(end) - dotByPlaneCoefficients(start))/(dotByPlaneCoefficients(firstRadialDirection)) center = vector.translate(start)(vector.scale(firstRadialDirection,t)) return circleArc(center, start, end)
def circleArcAroundPivotClosestPieces(pivot, start, end, smoothingFactor): pivotToStart = vector.translate(vector.minus(pivot))(start) pivotToEnd = vector.translate(vector.minus(pivot))(end) smallerNorm = min(vector.norm(pivotToStart),vector.norm(pivotToEnd)) def findActualEndPoint(vec): unitVec = vector.unit(vec) return vector.translate(pivot)(vector.scale(vector.unit(vec),smallerNorm*smoothingFactor)) circularPart = circleArcAroundPivot(pivot,findActualEndPoint(pivotToStart),findActualEndPoint(pivotToEnd)) #FIX!! if smallerNorm == vector.norm(pivotToStart): output = circularPart if smallerNorm != vector.norm(pivotToEnd): output.attachPartial(1, cutSegment(pivot, end, smallerNorm * smoothingFactor / vector.norm(pivotToEnd), smoothingFactor)) else: output = cutSegment(start, pivot, 1 - smoothingFactor, 1 - smallerNorm * smoothingFactor / vector.norm(pivotToStart)) output.attachPartial(1, circularPart) return output
def d(t): currentPoint = Wmap.ev(0)[0] currentLocationOnRnew = Rnew.projectOntoAxis(currentPoint) for x in pointsOnWmap: thisLocationOnRnew = Rnew.projectOntoAxis(x) if thisLocationOnRnew >= currentLocationOnRnew: if thisLocationOnRnew <= t: currentLocationOnRnew = thisLocationOnRnew currentPoint = x return vector.vectorToAngle(vector.unit(vector.translate(vector.minus(Rnew.ev(currentLocationOnRnew)[0]))(currentPoint)))
def circleArc(center, start, end): radToStart = vector.translate(vector.minus(center))(start) radToEnd = vector.translate(vector.minus(center))(end) radiusSquared = vector.norm(radToStart)*vector.norm(radToEnd) radius = math.sqrt(radiusSquared) innerProductValue = vector.innerproduct(radToStart, radToEnd) angle = math.acos(innerProductValue/radiusSquared) firstUnitRadial = vector.unit(radToStart) secondUnitRadial = vector.unit(vector.translate(vector.scale(radToStart,-innerProductValue/radiusSquared))(radToEnd)) def CN(t): point = vector.translate(center)(vector.translate(vector.scale(firstUnitRadial,radius*math.cos(t/radius)))(vector.scale(secondUnitRadial,radius*math.sin(t/radius)))) tangent = vector.translate(vector.scale(firstUnitRadial,-math.sin(t/radius)))(vector.scale(secondUnitRadial,math.cos(t/radius))) output = [point,tangent] #output.append([math.cos(t/radius),math.sin(t/radius),0]) return output return TwistingAxis(angle*radius,CN)
def boundarycompute(self): try: return self.boundary except: if self[0].str2[6:9] != 'GLY': atoms = self.findatoms( [" N ", " C ", " CA ", " O ", " OT1", " CB "]) else: atoms = self.findatoms( [" N ", " C ", " CA ", " O ", " OT1", " HA2"]) atoms.remove(0) posterm = vector.Nlocation(atoms[1].coords(), atoms[2].coords(), atoms[3].coords()) axis = vector.translate(vector.minus(atoms[0].coords()))(posterm) N1 = vector.unit(axis) length = vector.norm(axis) N2 = vector.unit( vector.translate(vector.minus(atoms[2].coords()))( atoms[4].coords())) self.boundary = [atoms[0].coords(), N1, N2, length] return self.boundary
def makeArray(self, dim1, dim2, distance1, distance2, antiparallel): for i in range(0,dim1): for j in range(0,dim2): if i == 0 and j == 0: output = copy.deepcopy(self) else: current = copy.deepcopy(self) if antiparallel and ((i + j)% 2 == 1): current.reverseOrbs() pointrigidMotion = vector.translate([i*distance1,j*distance2,0]) current.moveOrbs([pointrigidMotion, lambda x: x]) output.overlay(current) return output
def smoothedPieceWiseLinearFullFunctionality(points, mapFromSpaceToTime, Wnew, smoothingFactor = 0.33): if len(points) < 2: print("Error: only " + str(len(points)) + " points supplied to smoothedPieceWiseLinear") return currentPoints = copy.deepcopy(points) numPoints = len(currentPoints) attachElements = [cutSegment(points[0],points[1],0,smoothingFactor)] for i in range(0,numPoints - 2): lastToPivot = vector.translate(vector.minus(points[i]))(points[i+1]) pivotToNext = vector.translate(vector.minus(points[i+1]))(points[i+2]) angle = vector.innerproduct(lastToPivot, pivotToNext)/(vector.norm(lastToPivot)*vector.norm(pivotToNext)) collinear = (abs(angle) < 0.001) if collinear: attachElements.append(cutSegment(points[i],points[i+1],smoothingFactor,1)) attachElements.append(cutSegment(points[i+1],points[i+2],1,smoothingFactor)) else: attachElements.append(cutSegment(points[i],points[i+1],smoothingFactor,1-smoothingFactor)) attachElements.append(circleArcAroundPivotClosestPieces(points[i+1],points[i],points[i+2],smoothingFactor)) attachElements.append(cutSegment(points[-2],points[-1],smoothingFactor,1)) def iteratedAttach(start, end): if start < end: midpoint = (start + end)/2 iteratedAttach(start, midpoint) iteratedAttach(midpoint + 1, end) attachElements[start].attachPartial(1, attachElements[midpoint + 1]) iteratedAttach(0, len(attachElements)-1) Wmap = attachElements[0] produceN2 = lambda x : vector.unit(vector.orthogonalComponent(vector.translate(vector.minus(Wnew.ev(mapFromSpaceToTime(x[0]))[0]))(x[0]),x[1])) appendN2 = lambda x: [x[0],x[1],produceN2(x)] Wmap.CN = compose(appendN2,Wmap.CN) return [Wmap, Wnew, lambda t: mapFromSpaceToTime(Wmap.ev(t)[0])]
def segment(start, end): startToEnd = vector.translate(vector.minus(start))(end) distance = vector.norm(startToEnd) try: tng = vector.unit(startToEnd) def CN(t): output = [vector.translate(start)(vector.scale(tng,t)),tng] #output.append(normal) return output except: def CN(t): output = [start, [0,0,0]] return TwistingAxis(distance, CN)
def translate(self, x, y, z): self.vertices = vector.translate(self.vertices, x, y, z) self.invalidate_bounding_box() self.modified = True
def ev(self, t): return [vector.translate(vector.scale(self.tng,t))(self.start),self.tng,[0,0,0]]
def CN(t): point = vector.translate(center)(vector.translate(vector.scale(firstUnitRadial,radius*math.cos(t/radius)))(vector.scale(secondUnitRadial,radius*math.sin(t/radius)))) tangent = vector.translate(vector.scale(firstUnitRadial,-math.sin(t/radius)))(vector.scale(secondUnitRadial,math.cos(t/radius))) output = [point,tangent] #output.append([math.cos(t/radius),math.sin(t/radius),0]) return output
def findActualEndPoint(vec): unitVec = vector.unit(vec) return vector.translate(pivot)(vector.scale(vector.unit(vec),smallerNorm*smoothingFactor))
def CN(t): output = [vector.translate(start)(vector.scale(tng,t)),tng] #output.append(normal) return output
def cutSegment(start, end, startScale, endScale): segStart = vector.translate(start)(vector.scale(vector.translate(vector.minus(start))(end),startScale)) segEnd = vector.translate(start)(vector.scale(vector.translate(vector.minus(start))(end),endScale)) return segment(segStart, segEnd)