def curve_pos_and_speed(curve, x):
x1000 = x * 1000
for idx, (action, pts) in enumerate(curve.value):
if action in ["moveTo", "endPath", "closePath"]:
continue
last_action, last_pts = curve.value[idx - 1]
if action == "curveTo":
o = -1
a = last_pts[-1]
b, c, d = pts
if x1000 == a[0]:
o = a[1] / 1000
eb = a
ec = b
elif x1000 == d[0]:
o = d[1] / 1000
eb = c
ec = d
elif x1000 > a[0] and x1000 < d[0]:
e, f = splitCubic(a, b, c, d, x1000, isHorizontal=False)
ez, ea, eb, ec = e
o = ec[1] / 1000
else:
continue
tangent = math.degrees(
math.atan2(ec[1] - eb[1], ec[0] - eb[0]) + math.pi * .5)
#print(o, tangent)
if tangent >= 90:
t = (tangent - 90) / 90
else:
t = tangent / 90
if o != -1:
return o, t
raise Exception("No curve value found!")
def intersect(glyph, where, isHorizontal):
"""
Intersection of a glyph with a horizontal or vertical line.
Intersects each segment of a glyph using fontTools bezierTools.splitCubic and splitLine methods.
"""
pen = CollectSegmentsPen()
glyph.draw(pen)
nakedGlyph = pen.getSegments()
glyphIntersections = []
for i, contour in enumerate(nakedGlyph):
for segment in contour:
length = len(segment)
if length == 2:
pt1, pt2 = segment
returnedSegments = splitLine(pt1, pt2, where, int(isHorizontal))
elif length == 4:
pt1, pt2, pt3, pt4 = segment
returnedSegments = bezierTools.splitCubic(pt1, pt2, pt3, pt4, where, int(isHorizontal))
if len(returnedSegments) > 1:
intersectionPoints = findDuplicatePoints(returnedSegments)
if len(intersectionPoints):
box = calcBounds(segment)
intersectionPoints = [point for point in intersectionPoints if arrayTools.pointInRect(point, box)]
glyphIntersections.extend(intersectionPoints)
return glyphIntersections
def intersect(glyph, where, isHorizontal):
"""
Intersect a glyph with a horizontal or vertical line.
Intersect each segment of a glyph using fontTools bezierTools.splitCubic and splitLine methods.
"""
pen = CollectSegmentsPen(glyph.layer)
glyph.draw(pen)
nakedGlyph = pen.getSegments()
glyphIntersections = []
for i, contour in enumerate(nakedGlyph):
for segment in contour:
length = len(segment)
if length == 2:
pt1, pt2 = segment
returnedSegments = splitLine(pt1, pt2, where, int(isHorizontal))
elif length == 4:
pt1, pt2, pt3, pt4 = segment
returnedSegments = bezierTools.splitCubic(pt1, pt2, pt3, pt4, where, int(isHorizontal))
if len(returnedSegments) > 1:
intersectionPoints = findDuplicatePoints(returnedSegments)
if len(intersectionPoints):
box = calcBounds(segment)
intersectionPoints = [point for point in intersectionPoints if arrayTools.pointInRect(point, box)]
glyphIntersections.extend(intersectionPoints)
return glyphIntersections
def append_point_coordinate(contour, rpoints, where, is_horizontal):
""" Appends RPoint object to curve(RSegment object) by horizontal or vertical line.
Args:
contour:: RContour
The RContour object that you want to add RPoint object.
rpoints:: list
A list of RPoint objects. It should be containing 4 RPoint objects like
[startpoint, bcp(of startpoint), bcp(of endpoint), endpoint].
The order of start and end follows a index of contour.points.
where:: int or float
The coordinate value of line(x value if uses vertical line otherwise y value).
is_horizontal:: bool
If this is True, uses horizontal line(coordinate value of y).
Otherwise uses vertical line(coordinate value of x).
Raises:
arguments value error:: ValueError
If not found target segment in contour, raises this error.
This can be occured when the rpoints(RPoint objects) are not in the contour.points.
splitting error:: AssertionError
If function of splitting is not done properly, raises this error.
For example, if it split one line(or curve) but result is also one line(or curve).
"""
points = _r2t(rpoints)
new_curve = splitCubic(points[0], points[1], points[2], points[3], where,
is_horizontal)
assert (len(new_curve) > 1)
_append_point_curve(contour, rpoints, new_curve)
def test_splitCubic():
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=150,
isHorizontal=False) == [((0, 0), (25, 100), (75, 100), (100, 0))]
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=50,
isHorizontal=False) == [((0, 0), (12.5, 50), (31.25, 75), (50, 75)),
((50, 75), (68.75, 75), (87.5, 50), (100, 0))]
assert_curves_approx_equal(
splitCubic((0, 0), (25, 100), (75, 100), (100, 0),
where=25,
isHorizontal=True),
[((0, 0), (2.293792, 9.17517), (4.798045, 17.5085), (7.47414, 25)),
((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667),
(92.5259, 25)),
((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517),
(100, 1.77636e-15))])
def test_splitCubic():
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=150, isHorizontal=False
) == [((0, 0), (25, 100), (75, 100), (100, 0))]
assert splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=50, isHorizontal=False
) == [((0, 0), (12.5, 50), (31.25, 75), (50, 75)),
((50, 75), (68.75, 75), (87.5, 50), (100, 0))]
assert_curves_approx_equal(
splitCubic(
(0, 0), (25, 100), (75, 100), (100, 0), where=25,
isHorizontal=True),
[((0, 0), (2.293792, 9.17517), (4.798045, 17.5085), (7.47414, 25)),
((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667),
(92.5259, 25)),
((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517),
(100, 1.77636e-15))])
def _seg_ending_at(self, x):
x = clamp(self.minx, self.maxx, x)
# Draw a line at pt.x through the warp; the pt on the warp is be the desired offset
segments = splitCubic(*self.warp, x, False)
# no kinks/overlaps; there should be <=2 curves when split
# we are really just interested in there being only one unique start/end at pt.x
assert len(segments) <= 2, f"Too many segments: {segments}"
return segments[0]
def flagWarpVec(pt, accuracy=0.001):
# only active between warp[0].x and warp[-1].x
if pt.x < warp[0].x or pt.x > warp[-1].x:
print("Out of bounds:", pt)
return pt, Point(0, 0)
# Draw a line at pt.x through the warp; the pt on the warp is be the desired offset
segments = splitCubic(*warp, pt.x, False)
# no kinks/overlaps; there should be <=2 curves when split
# we are really just interested in there being only one unique start/end at pt.x
assert len(segments) <= 2, f"Too many segments: {segments}"
wpt = Point(*(segments[0][-1]))
deriv_pt = cubic_deriv_pos(1, *(Point(*s) for s in segments[0]))
return Point(0, wpt.y), deriv_pt
def splitWithAngle(curve, loc, axis):
# Split a curve at location y and return the location and angle
r = splitCubic(*curve, loc, isHorizontal=axis)
if len(r) == 2:
splitLoc = r[0][-1]
a = getAngle(r[0][-1], r[1][1]) # handle to handle
else:
# The location is either exatly on the end of the curve, or off the curve
# Return the angle and location either at the top or bottom
if loc >= curve[0][axis]:
splitLoc = curve[0]
a = getAngle(curve[0], curve[1])
else:
splitLoc = curve[-1]
a = getAngle(curve[-2], curve[-1])
if axis == 0:
a = 90 - a
return splitLoc, a
def _curveToOne(self, pt1, pt2, pt3):
hits = splitCubic(self.currentPt, pt1, pt2, pt3, self.value, self.isHorizontal)
for i in range(len(hits) - 1):
# a number of intersections is possible. Just take the
# last point of each segment.
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
if self.isHorizontal:
self.hits[self.contourIndex].append(round(hits[i][-1][0], 4))
else:
self.hits[self.contourIndex].append(round(hits[i][-1][1], 4))
if self.isHorizontal and pt3[1] == self.value:
# it could happen
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
self.hits[self.contourIndex].append(pt3[0])
if (not self.isHorizontal) and (pt3[0] == self.value):
# it could happen
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
self.hits[self.contourIndex].append(pt3[1])
self.currentPt = pt3
def _curveToOne(self, pt1, pt2, pt3):
hits = splitCubic(self.currentPt, pt1, pt2, pt3, self.value,
self.isHorizontal)
for i in range(len(hits) - 1):
# a number of intersections is possible. Just take the
# last point of each segment.
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
if self.isHorizontal:
self.hits[self.contourIndex].append(round(hits[i][-1][0], 4))
else:
self.hits[self.contourIndex].append(round(hits[i][-1][1], 4))
if self.isHorizontal and pt3[1] == self.value:
# it could happen
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
self.hits[self.contourIndex].append(pt3[0])
if (not self.isHorizontal) and (pt3[0] == self.value):
# it could happen
if self.contourIndex not in self.hits:
self.hits[self.contourIndex] = []
self.hits[self.contourIndex].append(pt3[1])
self.currentPt = pt3