def _BresTriBase(p0,p1,p2,dss_rerun=False, iscan_iline=None):
'''Do grunt work common to both Bresenham Triangle functions'''
borderPts = GetTriangleBorderPoints(p0,p1,p2)
if iscan_iline is not None:
iscan, iline = iscan_iline
return iscan, iline, borderPts
# Get the steepest dimension relative to every other dimension:
dSS = GetDirectionsOfSteepestSlope(p0,p1,p2)
dSS_notNone = [i for i in dSS if i!=None]
if len(dSS_notNone) == 0:
# Degenerate slope matrix (all 0's); points are collinear
return borderPts
iscan = getMostCommonVal(dSS_notNone)
if dss_rerun:
all_but = [i for i in range(len(p0)) if i != iscan]
p0a,p1a,p2a = fL([p0,p1,p2])[:, all_but]
dSS2 = GetDirectionsOfSteepestSlope(p0a,p1a,p2a)
dSS2_notNone = [i for i in dSS2 if i!=None]
iline = getMostCommonVal(dSS2_notNone)
if iline >= iscan:
iline += 1
else:
iline = dSS[iscan]
assert iline!=None, "iline is <flat>, that can't be right!"
return iscan, iline, borderPts
def _BresenhamTriangle_PlaneFormulaVersion(p0, p1, p2, iscan_iline=None): # Generalization for triangle
'''Bresenham N-D triangle rasterization
Uses a Bresenham-like algorithm, but uses floating-point
math and rounding for greater accuracy.
Holes are prevented by proper selection of dimensions:
the 'scan' dimension is fixed for each line (x')
the 'line' dimension has the maximum slope perpendicular to iscan (y')
All other dimensions are interpolated using the formula for a plane:
for three points (x0,y0,z0,...), (x1,y1,z1,...), (x2,y2,z2,...):
x = x0 + (x1-x0)*s + (x2-x0)*t
y = y0 + (y1-y0)*s + (y2-y0)*t
z = z0 + (z1-z0)*s + (z2-z0)*t
...
When 2 of these (x' and y') are fixed,
we can solve for s and t:
(here using A and B instead of x' and y'):
A = A0 + (A1-A0)*s + (A2-A0)*t
B = B0 + (B1-B0)*s + (B2-B0)*t
Using matrix form and with
dX01 = X1-X0 and dX02 = X2-X0:
[A - A0] = [dA01 dA02] * [s]
[B - B0] = [dB01 dB02] * [t]
We can solve by inverting tbe delta's matrix:
[s] = [dA01 dA02]^-1 * [A - A0]
[t] = [dB01 dB02] * [B - B0]
Lastly, we find values for all remaining coordinates (x,y,z,...) by plugging s and t back into the original equations and rounding the result.
'''
if p2==None:
return BresenhamFunction(p0,p1) # In case the last argument is None just use a plane...
p = np.array([p0,p1,p2])
iscan, iline, borderPts = _BresTriBase(p0,p1,p2,dss_rerun=False, iscan_iline=iscan_iline)
# Draw Bresenham lines to rasterize the triangle (draw along y' direction for each x' value)
minMaxList = _getMinMaxList(borderPts,iscan,iline)
# Get the points in the iscan/iline projection of the output:
minMaxProjected = fL(minMaxList)[:, :, (iscan, iline)]
projectedTriPts = _map_BresLines(minMaxProjected)
new_points = sample_points_from_plane(p, projectedTriPts, iscan, iline)
return new_points