def solve_collision(self, b1, b2):
# Changes the direction of non-static moving bodies, and separates overlapping bodies
def penetration(normal, movable_body, fixed_body):
if normal.x < -0.0001:
return abs(movable_body.rect.right() - fixed_body.rect.left())
elif normal.x > 0.0001:
return abs(fixed_body.rect.right() - movable_body.rect.left())
if normal.y < -0.0001:
return abs(fixed_body.rect.top() - movable_body.rect.bottom())
else:
return abs(movable_body.rect.top() - fixed_body.rect.bottom())
if b1.is_static and not (b2.is_static):
normal = self.calculate_normal(b2, b1)
pen_distance = penetration(normal, b2, b1)
b2.rect.position = vector.sum(b2.rect.position, vector.mul(normal, pen_distance))
b2.direction = vector.reflect(normal, b2.direction)
return normal
elif not (b1.is_static) and b2.is_static:
normal = self.calculate_normal(b1, b2)
pen_distance = penetration(normal, b1, b2)
b1.rect.position = vector.sum(b1.rect.position, vector.mul(normal, pen_distance))
b1.direction = vector.reflect(normal, b1.direction)
return normal
elif not (b1.is_static) and not (b2.is_static):
normal = self.calculate_normal(b1, b2)
normal_inv = vector.minus(normal)
pen_distance = penetration(normal, b1, b2)
b1.rect.set_pos(vector.sum(b1.rect.position, vector.mul(normal, 0.5 * pen_distance)))
b1.direction = vector.reflect(normal, b1.direction)
b2.rect.position = vector.sum(b2.rect.position, vector.mul(normal_inv, 0.5 * pen_distance))
b2.direction = vector.reflect(normal_inv, b2.get_direction())
return normal
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 detect_and_solve_collision(self):
# Detect and resolve collisions. Then, call collision callback functions.
for i in range(len(self.bodies) - 1):
for j in range(i + 1, len(self.bodies)):
if self.collide(self.bodies[i], self.bodies[j]):
normal = self.solve_collision(self.bodies[i], self.bodies[j])
for c in self.list_call_backs:
if self.bodies[i].object_type == c.tb1 and self.bodies[j].object_type == c.tb2:
c.call_back(self.bodies[i], self.bodies[j], normal)
elif self.bodies[j].object_type == c.tb1 and self.bodies[i].object_type == c.tb2:
c.call_back(self.bodies[j], self.bodies[i], vector.minus(normal))
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 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 dist(self, b, a=0):
""" Returns list with distribution of numbers between a to b, """
""" by number of bits in binary representation """
""" (optionally filtered by primality of sum of 1 bits). """
if (b < a or b < 0 or a < 0):
raise Exception
result = []
prev_bits = 0
if a > 0:
#TODO : optimizable by removing common bits
return vector.minus(self.dist(b), self.dist(a - 1))
else:
bl = bit.list(b)
l = len(bl)
for i, bt in zip(range(l, 0, -1), bl) + [(1, 1)]:
if bt:
additional = vector.shift(self.dist_get_cache(i - 1),
prev_bits)
if self.prefilter:
additional = self.primes.prime_mask(additional)
result = vector.add(result, additional)
prev_bits += 1
return result
def testMinus(self): self.assertEqual(vector.minus( [5, 7, 9], [4, 5, 6] ), [1, 2, 3] ) self.assertEqual(vector.minus( [5, 7, 9], [1, 2] ), [4, 5, 9] ) self.assertEqual(vector.minus( [1, 2], [5, 7, 9] ), [-4, -5, -9] )
import GF2 # version code ef5291f09f60+ coursera = 1 # Please fill out this stencil and submit using the provided submission script. # Some of the GF2 problems require use of the value GF2.one so the stencil imports it. from GF2 import one ## 1: (Problem 1) Vector Addition Practice 1 #Please express each answer as a list of numbers p1_v = [-1, 3] p1_u = [0, 4] p1_v_plus_u = vector.add(p1_v, p1_u) p1_v_minus_u = vector.minus(p1_v, p1_u) p1_three_v_minus_two_u = vector.minus(vector.scalar_mult(3, p1_v), vector.scalar_mult(2, p1_u)) ## 2: (Problem 2) Vector Addition Practice 2 p2_u = [-1, 1, 1] p2_v = [ 2, -1, 5] p2_v_plus_u = vector.add(p2_v, p2_u) p2_v_minus_u = vector.minus(p2_v, p2_u) p2_two_v_minus_u = vector.minus(vector.scalar_mult(2, p2_v), p2_u) p2_v_plus_two_u = vector.add(p2_v, vector.scalar_mult(2, p2_u)) ## 3: (Problem 3) Vector Addition Practice 3 p3_v = [GF2.zero, GF2.one, GF2.one] p3_u = [GF2.one, GF2.one, GF2.one] p3_vector_sum_1 = vector.add(p3_v, p3_u) p3_vector_sum_2 = vector.add(p3_v, p3_u, p3_u)
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)
def reverseOrbs(self):
temp = self.ev()
temp[1] = vector.minus(temp[1])
#temp[2] = vector.minus(temp[2])
self.CN = lambda x: temp