def evaltritangency(srfs, pts):
retval = irit.nil()
if (irit.ThisObject(srfs) == irit.SURFACE_TYPE):
srf1 = srfs
srf2 = srfs
srf3 = srfs
else:
srf1 = irit.nth(srfs, 1)
srf2 = irit.nth(srfs, 2)
srf3 = irit.nth(srfs, 3)
i = 1
while (i <= irit.SizeOf(pts)):
pt = irit.nth(pts, i)
irit.snoc(
irit.seval(srf1, irit.FetchRealObject(irit.coord(pt, 1)),
irit.FetchRealObject(irit.coord(pt, 2))) +
irit.seval(srf2, irit.FetchRealObject(irit.coord(pt, 3)),
irit.FetchRealObject(irit.coord(pt, 4))), retval)
irit.snoc(
irit.seval(srf1, irit.FetchRealObject(irit.coord(pt, 1)),
irit.FetchRealObject(irit.coord(pt, 2))) +
irit.seval(srf3, irit.FetchRealObject(irit.coord(pt, 5)),
irit.FetchRealObject(irit.coord(pt, 6))), retval)
irit.snoc(
irit.seval(srf2, irit.FetchRealObject(irit.coord(pt, 3)),
irit.FetchRealObject(irit.coord(pt, 4))) +
irit.seval(srf3, irit.FetchRealObject(irit.coord(pt, 5)),
irit.FetchRealObject(irit.coord(pt, 6))), retval)
i = i + 1
return retval
def evalonebitangency(srfs, pts):
ruling = irit.nil()
tmp1pts = irit.nil()
tmp2pts = irit.nil()
if (irit.ThisObject(srfs) == irit.SURFACE_TYPE):
srf1 = srfs
srf2 = srfs
else:
srf1 = irit.nth(srfs, 1)
srf2 = irit.nth(srfs, 2)
i = 1
while (i <= irit.SizeOf(pts)):
pt = irit.nth(pts, i)
pt1 = irit.seval(srf1, irit.FetchRealObject(irit.coord(pt, 1)),
irit.FetchRealObject(irit.coord(pt, 2)))
pt2 = irit.seval(srf2, irit.FetchRealObject(irit.coord(pt, 3)),
irit.FetchRealObject(irit.coord(pt, 4)))
irit.snoc(pt1 + pt2, ruling)
irit.snoc(pt1 * irit.tx(0), tmp1pts)
irit.snoc(pt2 * irit.tx(0), tmp2pts)
i = i + 1
irit.attrib(ruling, "rgb", irit.GenStrObject("255, 128, 128"))
if (irit.SizeOf(tmp1pts) > 1 and irit.SizeOf(tmp2pts) > 1):
tmp1pts = irit.poly(tmp1pts, irit.TRUE)
tmp2pts = irit.poly(tmp2pts, irit.TRUE)
irit.attrib(tmp1pts, "rgb", irit.GenStrObject("128, 255, 128"))
irit.attrib(tmp2pts, "rgb", irit.GenStrObject("128, 255, 128"))
retval = irit.list(ruling, tmp1pts, tmp2pts)
else:
retval = irit.nil()
return retval
def dominos(path, scl, piecetimestep):
retval = irit.nil()
animtime = 0
dominopiece = irit.box(
(-0.01, -0.006, 0), 0.02, 0.006, 0.05) * irit.sc(scl)
rot_x = irit.cbezier( irit.list( irit.ctlpt( irit.E1, 0 ), \
irit.ctlpt( irit.E1, 80 ) ) )
crvdomain = irit.pdomain(path)
t = irit.FetchRealObject(irit.nth(crvdomain, 1))
dpath = irit.cderive(path)
while (t < irit.FetchRealObject(irit.nth(crvdomain, 2))):
d = irit.Fetch3TupleObject(
irit.coerce(irit.ceval(dpath, t), irit.POINT_TYPE))
dlen = math.sqrt(DotProd(d, d))
rot_x = irit.creparam(rot_x, animtime, animtime + piecetimestep)
irit.attrib(dominopiece, "animation", irit.list(rot_x))
irit.setname(irit.getattr(dominopiece, "animation"), 0, "rot_x")
dp = dominopiece * irit.rz(
-math.atan2(d[0], d[1]) * 180 / math.pi) * irit.trans(
irit.Fetch3TupleObject(
irit.coerce(irit.ceval(path, t), irit.VECTOR_TYPE)))
irit.snoc(dp, retval)
t = t + 0.04 * scl / dlen
animtime = animtime + piecetimestep * 0.6
return retval
def srfframecrvs(srf, width):
umin = irit.nth(irit.pdomain(srf), 1)
umax = irit.nth(irit.pdomain(srf), 2)
vmin = irit.nth(irit.pdomain(srf), 3)
vmax = irit.nth(irit.pdomain(srf), 4)
retval = irit.list(
irit.swpcircsrf(
irit.csurface(srf, irit.COL, irit.FetchRealObject(umin)), width,
0),
irit.swpcircsrf(
irit.csurface(srf, irit.COL,
irit.FetchRealObject((umin + umax) / 2.0)), width,
0),
irit.swpcircsrf(
irit.csurface(srf, irit.COL, irit.FetchRealObject(umax)), width,
0),
irit.swpcircsrf(
irit.csurface(srf, irit.ROW, irit.FetchRealObject(vmin)), width,
0),
irit.swpcircsrf(
irit.csurface(srf, irit.ROW,
irit.FetchRealObject((vmin + vmax) / 2.0)), width,
0),
irit.swpcircsrf(
irit.csurface(srf, irit.ROW, irit.FetchRealObject(vmax)), width,
0))
return retval
def antanim(scl):
save_res = irit.GetResolution()
bodyall = antbody()
body = irit.nth(bodyall, 1)
eyes = irit.nth(bodyall, 2)
llegs = irit.list(
antlleganim(1) * irit.sc(1.1) * irit.sx(1.3) * irit.ry(
(-45)) * irit.trans((0.1, 0, 1.02)),
antlleganim((-1)) * irit.sc(1.3) * irit.ry(10) * irit.trans(
(0.1, 0.05, 1)),
antlleganim(1) * irit.sc(1.2) * irit.sx(1.4) * irit.ry(40) *
irit.trans((0.1, 0.02, 0.95)))
rlegs = irit.list(
antrleganim(
(-1)) * irit.sc(1.1) * irit.sx(1.3) * irit.ry(45) * irit.trans(
((-0.1), 0, 1.02)),
antrleganim(1) * irit.sc(1.3) * irit.ry((-10)) * irit.trans(
((-0.1), 0.05, 1)),
antrleganim((-1)) * irit.sc(1.2) * irit.sx(1.4) * irit.ry(
(-40)) * irit.trans(((-0.1), 0.02, 0.95)))
irit.SetResolution(20)
antennas = irit.list(
antantenna() * irit.ry((-110)) * irit.trans(((-0.02), 0.2, 1.6)),
antantenna() * irit.ry((-70)) * irit.trans((0.02, 0.2, 1.6)))
irit.attrprop(antennas, "u_resolution", irit.GenRealObject(0.2))
body = (body + irit.gpolygon(antennas, 1))
irit.attrib(body, "rgb", irit.GenStrObject("255,50,50"))
irit.SetResolution(save_res)
retval = irit.list(
body, llegs, rlegs,
eyes) * irit.sz(1.3) * irit.sc(1) * irit.ty(0.28785) * irit.rx(90)
mov_y = irit.creparam( irit.ctlpt( irit.E1, 0 ) + \
irit.ctlpt( irit.E1, (-1 ) ), 0, 1.2 )
irit.attrib(retval, "animation", mov_y)
return retval
def positioncurvature(srf, u, v):
eps = 1e-012
c = irit.circle((0, 0, 0), 1)
k = irit.scrvtreval(srf, u, v, 1)
r1 = irit.max(
irit.min(1.0 / (irit.FetchRealObject(irit.nth(k, 1)) + eps), 1000),
(-1000))
r2 = irit.max(
irit.min(1.0 / (irit.FetchRealObject(irit.nth(k, 3)) + eps), 1000),
(-1000))
v1 = irit.nth(k, 2)
v2 = irit.nth(k, 4)
p = irit.seval(srf, u, v)
n = irit.snormal(srf, u, v)
d1 = v1 ^ n
d2 = v2 ^ n
c1 = c * \
irit.sc( r1 ) * \
irit.rotz2v( irit.Fetch3TupleObject(d1) ) * \
irit.trans( irit.Fetch3TupleObject(irit.coerce( p, irit.VECTOR_TYPE ) + n * r1 ))
c2 = c * \
irit.sc( r2 ) * \
irit.rotz2v( irit.Fetch3TupleObject(d2) ) * \
irit.trans( irit.Fetch3TupleObject(irit.coerce( p, irit.VECTOR_TYPE ) + n * r2) )
retval = irit.list(
p, c1, c2,
p + irit.coerce(irit.coerce(p, irit.POINT_TYPE) + v1, irit.E3),
p + irit.coerce(irit.coerce(p, irit.POINT_TYPE) + v2, irit.E3),
positionasymptotes(srf, u, v))
irit.adwidth(retval, 2)
irit.color(retval, irit.YELLOW)
return retval
def ant(scl):
save_res = irit.GetResolution()
bodyall = antbody()
body = irit.nth(bodyall, 1)
eyes = irit.nth(bodyall, 2)
leg = antleg()
llegs = irit.list(
leg * irit.sc(1.1) * irit.sx(1.3) * irit.ry((-45)) * irit.trans(
(0.1, 0, 1.02)),
leg * irit.sc(1.3) * irit.ry(10) * irit.trans((0.1, 0.05, 1)),
leg * irit.sc(1.2) * irit.sx(1.4) * irit.ry(40) * irit.trans(
(0.1, 0.02, 0.95)))
irit.SetResolution(20)
irit.attrprop(llegs, "u_resolution", irit.GenRealObject(0.2))
antennas = irit.list(
antantenna() * irit.ry((-110)) * irit.trans(((-0.02), 0.2, 1.6)),
antantenna() * irit.ry((-70)) * irit.trans((0.02, 0.2, 1.6)))
irit.attrprop(antennas, "u_resolution", irit.GenRealObject(0.2))
body = (body + irit.gpolygon(llegs, 1) + irit.gpolygon(llegs, 1) * irit.sx(
(-1)) + irit.gpolygon(antennas, 1))
irit.attrib(body, "rgb", irit.GenStrObject("255,50,50"))
irit.SetResolution(save_res)
retval = irit.list(
body,
eyes) * irit.sz(1.3) * irit.sc(1) * irit.ty(0.28785) * irit.rx(90)
return retval
def printspeedchanges( str, crv ):
dc = irit.cderive( crv )
speedsqr = irit.bbox( irit.symbdprod( dc, dc ) )
irit.printf( "%s [%f %f]\n",
irit.list( str,
asqrt( irit.FetchRealObject(irit.nth( speedsqr, 1 )) ),
asqrt( irit.FetchRealObject(irit.nth( speedsqr, 2 )) ) ) )
def makebboxunit(obj):
b = irit.bbox(obj)
xmin = irit.FetchRealObjecy(irit.nth(b, 1))
xmax = irit.nth(b, 2)
ymin = irit.nth(b, 3)
ymax = irit.nth(b, 4)
retval = obj * irit.tx((-xmin)) * irit.ty(
(-ymin)) * irit.sx(1.0 / (xmax - xmin)) * irit.sy(1.0 / (ymax - ymin))
return retval
def cnvrtcrvs2domains( crvs, theta ):
retval = irit.nil( )
i = 1
while ( i <= irit.SizeOf( crvs ) ):
dm = irit.pdomain( irit.nth( crvs, i ) )
irit.snoc( irit.ctlpt( irit.E2, theta, irit.nth( dm, 1 ) ) + \
irit.ctlpt( irit.E2, theta, irit.nth( dm, 2 ) ), retval )
i = i + 1
return retval
def makepolylines(listofctlpts):
retval = irit.nil()
i = 1
while (i <= irit.SizeOf(listofctlpts)):
pl = irit.nth(listofctlpts, i)
if (irit.SizeOf(pl) > 1):
irit.snoc(irit.poly(irit.nth(listofctlpts, i), 1), retval)
i = i + 1
return retval
def printsurface( srf ):
orders = irit.fforder( srf )
msize = irit.ffmsize( srf )
irit.printf( "surface of orders %d x %d, mesh size %d x %d and point type %s\n", orders + msize + irit.list( getpointtype( irit.coord( srf, 0 ) ) ) )
irit.printf( "control mesh:\n", irit.nil( ) )
printctlmesh( srf )
if ( 1 ):
kvs = irit.ffkntvec( srf )
printknotvector( "u ", irit.nth( kvs, 1 ) )
printknotvector( "v ", irit.nth( kvs, 2 ) )
def evaltv(tv, ulen, vlen, wlen):
retval = irit.nil()
dom = irit.pdomain(tv)
i = 0
while (i <= ulen - 1):
u = irit.FetchRealObject(irit.nth(dom, 1)) + i * irit.FetchRealObject(
irit.nth(dom, 2) - irit.nth(dom, 1)) / float(ulen - 1)
lst2 = irit.nil()
j = 0
while (j <= vlen - 1):
v = irit.FetchRealObject(irit.nth(
dom, 3)) + j * irit.FetchRealObject(
irit.nth(dom, 4) - irit.nth(dom, 3)) / float(vlen - 1)
lst3 = irit.nil()
k = 0
while (k <= wlen - 1):
w = irit.FetchRealObject(irit.nth(
dom, 5)) + k * irit.FetchRealObject(
irit.nth(dom, 6) - irit.nth(dom, 5)) / float(wlen - 1)
irit.snoc(irit.teval(tv, u, v, w), lst3)
k = k + 1
irit.snoc(lst3 * irit.tx(0), lst2)
j = j + 1
irit.snoc(lst2 * irit.tx(0), retval)
i = i + 1
retval = irit.tbezier(retval)
return retval
def printtrivar( tv ):
orders = irit.fforder( tv )
msize = irit.ffmsize( tv )
irit.printf( "trivar of orders %d x %d x %d mesh size %d x %d x %d and point type %s\n", orders + msize + irit.list( getpointtype( irit.coord( tv, 0 ) ) ) )
irit.printf( "control mesh:\n", irit.nil( ) )
printctlmesh( tv )
if ( 1 ):
kvs = irit.ffkntvec( tv )
printknotvector( "u ", irit.nth( kvs, 1 ) )
printknotvector( "v ", irit.nth( kvs, 2 ) )
printknotvector( "w ", irit.nth( kvs, 3 ) )
def testinter(s1, s2):
retval = irit.ssintr2(s1, s2, step, subdivtol, numerictol, euclidean)
if (irit.SizeOf(retval) == 2):
n = (irit.SizeOf(irit.nth(retval, 1)) +
irit.SizeOf(irit.nth(retval, 2))) / 2.0
else:
if (irit.SizeOf(retval) == 1):
n = irit.SizeOf(irit.nth(retval, 1)) / 2.0
else:
n = 0
irit.printf("found %d intersection connected components.\n", irit.list(n))
return retval
def originalf(f, newf, deg, c, ptype):
net = irit.nil()
f_p = irit.coerce(f, irit.POWER_TYPE)
tmp = irit.ffsplit(f_p)
tmp3 = irit.ffsplit(newf)
i = 1
while (i <= c):
t = irit.coord(irit.coord(irit.nth(tmp, i), deg), 1)
tmp2 = irit.nth(tmp3, i) * irit.sc(irit.FetchRealObject(t))
irit.snoc(irit.coerce(tmp2, irit.E1), net)
i = i + 1
retval = irit.ffmerge(net, ptype)
return retval
def polesfree(srf, dpth, tmin, tmax):
if (irit.ffpoles(srf) == 0):
retval = irit.list(srf)
else:
if (dpth <= 0):
retval = irit.nil()
else:
t = (tmin + tmax) / 2
srfs = irit.sdivide(srf, irit.ROW, t)
retval = irit.polesfree(irit.nth(srfs, 1), dpth - 1, tmin,
t) + irit.polesfree(
irit.nth(srfs, 2), dpth - 1, t, tmax)
return retval
def computeoptimalmotion(theta1, theta2, phi1, phi2, eps):
err = estimatesphericalcrv(theta1, theta2, phi1, phi2)
irit.printf(" %12g %12g %12g %12g = %f\n",
irit.list(theta1, theta2, phi1, phi2, err))
if (err > eps):
newpt = midgreatcircpt(theta1, theta2, phi1, phi2)
theta = irit.FetchRealObject(irit.nth(newpt, 1))
phi = irit.FetchRealObject(irit.nth(newpt, 2))
retval = computeoptimalmotion(theta, theta2, phi, phi2,
eps) + computeoptimalmotion(
theta1, theta, phi1, phi, eps)
else:
retval = irit.list(computesphericalcrv(theta1, theta2, phi1, phi2))
return retval
def lj8samplecurve(crv, n):
ptl = irit.nil()
t0 = irit.nth(irit.pdomain(crv), 1)
t1 = irit.nth(irit.pdomain(crv), 2)
if (n < 2):
n = 2
dt = (t1 - t0) / (n + 0.0001 - 1)
t = t0
while (t <= t1):
pt = irit.ceval(crv, irit.FetchRealObject(t))
irit.snoc(pt, ptl)
t = t + dt
retval = ptl
return retval
def printctlmeshaux( mesh, ofst, dims ):
if ( irit.SizeOf( dims ) == 1 ):
i = 1
while ( i <= irit.FetchRealObject(irit.nth( dims, 1 )) ):
printctlpoint( irit.nth( mesh, i + ofst ) )
i = i + 1
irit.printf( "\n", irit.nil( ) )
else:
dimsl = getlistwithoutlast( dims )
d1 = getlistlast( dims )
d2 = getlistproduct( dimsl )
i = 1
while ( i <= irit.FetchRealObject(d1) ):
printctlmeshaux( mesh, ofst + d2 * ( i - 1 ), dimsl )
i = i + 1
def raytraptris3d(srfs, subeps, numeps):
pts = irit.raytraps(srfs, 1, subeps, numeps, 1)
retval = irit.nil()
if (irit.SizeOf(pts) > 1):
irit.printf("%d solution(s) found\n", irit.list(irit.SizeOf(pts)))
i = 1
while (i <= irit.SizeOf(pts)):
pt = irit.coord(pts, i)
err = irit.getattr(pt, "rngerror")
if (irit.ThisObject(err) == irit.NUMERIC_TYPE):
irit.printf("error = %16.14f\n", irit.list(err))
else:
irit.printf("error is not provided\n", irit.nil())
points = irit.nil()
j = 1
while (j <= irit.SizeOf(srfs)):
irit.snoc(
irit.seval(
irit.nth(srfs, j),
irit.FetchRealObject(irit.coord(pt, 1 + (j - 1) * 2)),
irit.FetchRealObject(irit.coord(pt, 2 + (j - 1) * 2))),
points)
j = j + 1
irit.snoc(irit.poly(points, 0), retval)
i = i + 1
return retval
def interptseval(crvs):
retval = irit.nil()
i = 1
while (i <= irit.SizeOf(crvs)):
crv = irit.nth(crvs, i)
interpts = irit.getattr(crv, "interpts")
j = 1
while (j <= irit.SizeOf(interpts)):
irit.snoc(
irit.ceval(crv, irit.FetchRealObject(irit.nth(interpts, j))),
retval)
j = j + 1
i = i + 1
irit.printf("numer of intersections detected = %d\n",
irit.list(irit.SizeOf(retval)))
return retval
def printknotvector( str, kv ):
irit.printf( " [%sknotvector:", irit.list( str ) )
i = 1
while ( i <= irit.SizeOf( kv ) ):
irit.printf( " %-.6lg", irit.list( irit.nth( kv, i ) ) )
i = i + 1
irit.printf( "]\n", irit.nil( ) )
def getlistproduct( lst ):
retval = 1
i = 1
while ( i <= irit.SizeOf( lst ) ):
retval = retval * irit.FetchRealObject(irit.nth( lst, i ))
i = i + 1
return retval
def getlistwithoutlast( lst ):
retval = irit.nil( )
i = 1
while ( i <= irit.SizeOf( lst ) - 1 ):
irit.snoc( irit.nth( lst, i ), retval )
i = i + 1
return retval
def evalantipodalptsonsrf( srf ):
aps = irit.antipodal( srf, 0.001, (-1e-012 ) )
irit.printf( "%d antipodal points detected\n", irit.list( irit.SizeOf( aps ) ) )
retval = irit.nil( )
diam = 0
i = 1
while ( i <= irit.SizeOf( aps ) ):
ap = irit.nth( aps, i )
u1 = irit.coord( ap, 1 )
v1 = irit.coord( ap, 2 )
u2 = irit.coord( ap, 3 )
v2 = irit.coord( ap, 4 )
pt1 = irit.seval( srf, irit.FetchRealObject(u1), irit.FetchRealObject(v1) )
pt2 = irit.seval( srf, irit.FetchRealObject(u2), irit.FetchRealObject(v2) )
if ( irit.dstptpt( irit.coerce( pt1, irit.POINT_TYPE ),
irit.coerce( pt2, irit.POINT_TYPE ) ) > diam ):
diam = irit.dstptpt( irit.coerce( pt1, irit.POINT_TYPE ),
irit.coerce( pt2, irit.POINT_TYPE ) )
diamline = pt1 + pt2
irit.snoc( irit.list( pt1 + pt2, pt1 * irit.tx( 0 ), pt2 * irit.tx( 0 ) ), retval )
i = i + 1
irit.color( retval, irit.YELLOW )
irit.color( diamline, irit.CYAN )
irit.adwidth( diamline, 3 )
irit.snoc( irit.list( diamline ), retval )
return retval
def animbisectcrv2( crv1, crv2, data, cntr ):
irit.color( crv1, irit.YELLOW )
irit.color( crv2, irit.YELLOW )
irit.adwidth( crv1, 4 )
irit.adwidth( crv2, 4 )
i = 0
while ( i <= irit.SizeOf( cntr ) - 1 ):
pt = irit.coord( cntr, i )
pt1 = irit.ceval( crv1, irit.FetchRealObject(irit.coord( pt, 0 ) ))
pt2 = irit.ceval( crv2, irit.FetchRealObject(irit.coord( pt, 1 ) ))
nrml1 = cnormalplnr( crv1, irit.coord( pt, 0 ) )
nrml2 = cnormalplnr( crv2, irit.coord( pt, 1 ) )
aaa = irit.ptslnln( irit.Fetch3TupleObject(irit.coerce( pt1, irit.POINT_TYPE )),
irit.Fetch3TupleObject(nrml1),
irit.Fetch3TupleObject(irit.coerce( pt2, irit.POINT_TYPE )),
irit.Fetch3TupleObject(nrml2 ))
if (irit.IsNullObject(aaa)):
interpt = irit.GenNullObject();
else:
interpt = irit.nth( aaa, 1 )
if ( irit.ThisObject(interpt) == irit.POINT_TYPE ):
irit.color( pt1, irit.GREEN )
irit.color( pt2, irit.GREEN )
irit.color( interpt, irit.WHITE )
bisectlns = irit.coerce( pt1, irit.E2 ) + irit.coerce( interpt, irit.E2 ) + irit.coerce( pt2, irit.E2 )
irit.color( bisectlns, irit.MAGENTA )
if ( irit.FetchRealObject(irit.coord( interpt, 1 )) < 10 and \
irit.FetchRealObject(irit.coord( interpt, 1 )) > (-10 ) and \
irit.FetchRealObject(irit.coord( interpt, 2 )) < 10 and \
irit.FetchRealObject(irit.coord( interpt, 2 )) > (-10 ) ):
irit.view( irit.list( crv1, crv2, data, pt1, pt2, interpt, \
bisectlns ), irit.ON )
i = i + 1
def srflistframecrvs(srflist, width):
retval = irit.nil()
i = 1
while (i <= irit.SizeOf(srflist)):
retval = retval + srfframecrvs(irit.nth(srflist, i), width)
i = i + 1
return retval
def offsetcrvlist( clst, ofst ):
retval = irit.nil( )
i = 1
while ( i <= irit.SizeOf( clst ) ):
irit.snoc( irit.offset( irit.nth( clst, i ), irit.GenRealObject(ofst), 1e-006, 1 ), retval )
i = i + 1
return retval
def getbisectpt( crv1, crv2, pt ):
pt1 = irit.ceval( crv1, irit.FetchRealObject(irit.coord( pt, 0 ) ))
pt2 = irit.ceval( crv2, irit.FetchRealObject(irit.coord( pt, 1 ) ))
nrml1 = irit.cnormalplnr( crv1, irit.FetchRealObject(irit.coord( pt, 0 ) ))
nrml2 = irit.cnormalplnr( crv2, irit.FetchRealObject(irit.coord( pt, 1 ) ))
interpts = irit.ptslnln( irit.coerce( pt1, irit.POINT_TYPE ), nrml1, irit.coerce( pt2, irit.POINT_TYPE ), nrml2 )
retval = irit.nth( interpts, 1 )
return retval
