Nothing
xsplineTangent.s1pos.s2neg.A0.noA3.x <- function(px0, px1, px2, px3, py0, py1, py2, py3, s1, s2, t) {
(((((1/(-1 - s1) * ((t - s1)/(-1 - s1)) + ((t - s1)/(-1 -
s1)) * (1/(-1 - s1))) * ((t - s1)/(-1 - s1)) + ((t - s1)/(-1 -
s1)) * ((t - s1)/(-1 - s1)) * (1/(-1 - s1))) * (10 - (2 *
(-1 - s1) * (-1 - s1)) + (2 * (2 * (-1 - s1) * (-1 - s1)) -
15) * ((t - s1)/(-1 - s1)) + (6 - (2 * (-1 - s1) * (-1 -
s1))) * ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1))) + ((t -
s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) *
((2 * (2 * (-1 - s1) * (-1 - s1)) - 15) * (1/(-1 - s1)) +
((6 - (2 * (-1 - s1) * (-1 - s1))) * (1/(-1 - s1)) *
((t - s1)/(-1 - s1)) + (6 - (2 * (-1 - s1) * (-1 -
s1))) * ((t - s1)/(-1 - s1)) * (1/(-1 - s1))))) *
px0 - ((1 - t) * ((1 - t) * ((1 - t) * ((1 - t) * (4 - 5 *
(-s2)) + (14 * (-s2) - 11 + (1 - t) * (4 - 5 * (-s2)))) +
(8 - 12 * (-s2) + (1 - t) * (14 * (-s2) - 11 + (1 - t) *
(4 - 5 * (-s2))))) + (2 * (-s2) + (1 - t) * (8 - 12 *
(-s2) + (1 - t) * (14 * (-s2) - 11 + (1 - t) * (4 - 5 * (-s2)))))) +
((-s2) + (1 - t) * (2 * (-s2) + (1 - t) * (8 - 12 * (-s2) +
(1 - t) * (14 * (-s2) - 11 + (1 - t) * (4 - 5 * (-s2))))))) *
px1 + (((1/(1 + s1) * ((t + s1)/(1 + s1)) + ((t + s1)/(1 +
s1)) * (1/(1 + s1))) * ((t + s1)/(1 + s1)) + ((t + s1)/(1 +
s1)) * ((t + s1)/(1 + s1)) * (1/(1 + s1))) * (10 - (2 * (1 +
s1) * (1 + s1)) + (2 * (2 * (1 + s1) * (1 + s1)) - 15) *
((t + s1)/(1 + s1)) + (6 - (2 * (1 + s1) * (1 + s1))) * ((t +
s1)/(1 + s1)) * ((t + s1)/(1 + s1))) + ((t + s1)/(1 + s1)) *
((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) * ((2 * (2 * (1 +
s1) * (1 + s1)) - 15) * (1/(1 + s1)) + ((6 - (2 * (1 + s1) *
(1 + s1))) * (1/(1 + s1)) * ((t + s1)/(1 + s1)) + (6 - (2 *
(1 + s1) * (1 + s1))) * ((t + s1)/(1 + s1)) * (1/(1 + s1))))) *
px2 + (((-s2) + (t - 1) * (2 * (-s2) + (t - 1) * (t - 1) *
(-2 * (-s2) - (t - 1) * (-s2)))) + (t - 1) * ((2 * (-s2) +
(t - 1) * (t - 1) * (-2 * (-s2) - (t - 1) * (-s2))) + (t -
1) * (((t - 1) + (t - 1)) * (-2 * (-s2) - (t - 1) * (-s2)) -
(t - 1) * (t - 1) * (-s2)))) * px3)/(((t - s1)/(-1 - s1)) *
((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) * (10 - (2 *
(-1 - s1) * (-1 - s1)) + (2 * (2 * (-1 - s1) * (-1 - s1)) -
15) * ((t - s1)/(-1 - s1)) + (6 - (2 * (-1 - s1) * (-1 -
s1))) * ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1))) + (1 -
t) * ((-s2) + (1 - t) * (2 * (-s2) + (1 - t) * (8 - 12 *
(-s2) + (1 - t) * (14 * (-s2) - 11 + (1 - t) * (4 - 5 * (-s2)))))) +
((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) * ((t + s1)/(1 +
s1)) * (10 - (2 * (1 + s1) * (1 + s1)) + (2 * (2 * (1 +
s1) * (1 + s1)) - 15) * ((t + s1)/(1 + s1)) + (6 - (2 *
(1 + s1) * (1 + s1))) * ((t + s1)/(1 + s1)) * ((t + s1)/(1 +
s1))) + (t - 1) * ((-s2) + (t - 1) * (2 * (-s2) + (t -
1) * (t - 1) * (-2 * (-s2) - (t - 1) * (-s2))))) - (((t -
s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) *
(10 - (2 * (-1 - s1) * (-1 - s1)) + (2 * (2 * (-1 - s1) *
(-1 - s1)) - 15) * ((t - s1)/(-1 - s1)) + (6 - (2 * (-1 -
s1) * (-1 - s1))) * ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 -
s1))) * px0 + (1 - t) * ((-s2) + (1 - t) * (2 * (-s2) +
(1 - t) * (8 - 12 * (-s2) + (1 - t) * (14 * (-s2) - 11 +
(1 - t) * (4 - 5 * (-s2)))))) * px1 + ((t + s1)/(1 +
s1)) * ((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) * (10 -
(2 * (1 + s1) * (1 + s1)) + (2 * (2 * (1 + s1) * (1 + s1)) -
15) * ((t + s1)/(1 + s1)) + (6 - (2 * (1 + s1) * (1 + s1))) *
((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1))) * px2 + (t - 1) *
((-s2) + (t - 1) * (2 * (-s2) + (t - 1) * (t - 1) * (-2 *
(-s2) - (t - 1) * (-s2)))) * px3) * (((1/(-1 - s1) *
((t - s1)/(-1 - s1)) + ((t - s1)/(-1 - s1)) * (1/(-1 - s1))) *
((t - s1)/(-1 - s1)) + ((t - s1)/(-1 - s1)) * ((t - s1)/(-1 -
s1)) * (1/(-1 - s1))) * (10 - (2 * (-1 - s1) * (-1 - s1)) +
(2 * (2 * (-1 - s1) * (-1 - s1)) - 15) * ((t - s1)/(-1 -
s1)) + (6 - (2 * (-1 - s1) * (-1 - s1))) * ((t - s1)/(-1 -
s1)) * ((t - s1)/(-1 - s1))) + ((t - s1)/(-1 - s1)) * ((t -
s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) * ((2 * (2 * (-1 -
s1) * (-1 - s1)) - 15) * (1/(-1 - s1)) + ((6 - (2 * (-1 -
s1) * (-1 - s1))) * (1/(-1 - s1)) * ((t - s1)/(-1 - s1)) +
(6 - (2 * (-1 - s1) * (-1 - s1))) * ((t - s1)/(-1 - s1)) *
(1/(-1 - s1)))) - ((1 - t) * ((1 - t) * ((1 - t) * ((1 -
t) * (4 - 5 * (-s2)) + (14 * (-s2) - 11 + (1 - t) * (4 -
5 * (-s2)))) + (8 - 12 * (-s2) + (1 - t) * (14 * (-s2) -
11 + (1 - t) * (4 - 5 * (-s2))))) + (2 * (-s2) + (1 - t) *
(8 - 12 * (-s2) + (1 - t) * (14 * (-s2) - 11 + (1 - t) *
(4 - 5 * (-s2)))))) + ((-s2) + (1 - t) * (2 * (-s2) +
(1 - t) * (8 - 12 * (-s2) + (1 - t) * (14 * (-s2) - 11 +
(1 - t) * (4 - 5 * (-s2))))))) + (((1/(1 + s1) * ((t +
s1)/(1 + s1)) + ((t + s1)/(1 + s1)) * (1/(1 + s1))) * ((t +
s1)/(1 + s1)) + ((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) *
(1/(1 + s1))) * (10 - (2 * (1 + s1) * (1 + s1)) + (2 * (2 *
(1 + s1) * (1 + s1)) - 15) * ((t + s1)/(1 + s1)) + (6 - (2 *
(1 + s1) * (1 + s1))) * ((t + s1)/(1 + s1)) * ((t + s1)/(1 +
s1))) + ((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) * ((t +
s1)/(1 + s1)) * ((2 * (2 * (1 + s1) * (1 + s1)) - 15) * (1/(1 +
s1)) + ((6 - (2 * (1 + s1) * (1 + s1))) * (1/(1 + s1)) *
((t + s1)/(1 + s1)) + (6 - (2 * (1 + s1) * (1 + s1))) * ((t +
s1)/(1 + s1)) * (1/(1 + s1))))) + (((-s2) + (t - 1) * (2 *
(-s2) + (t - 1) * (t - 1) * (-2 * (-s2) - (t - 1) * (-s2)))) +
(t - 1) * ((2 * (-s2) + (t - 1) * (t - 1) * (-2 * (-s2) -
(t - 1) * (-s2))) + (t - 1) * (((t - 1) + (t - 1)) *
(-2 * (-s2) - (t - 1) * (-s2)) - (t - 1) * (t - 1) *
(-s2)))))/(((t - s1)/(-1 - s1)) * ((t - s1)/(-1 - s1)) *
((t - s1)/(-1 - s1)) * (10 - (2 * (-1 - s1) * (-1 - s1)) +
(2 * (2 * (-1 - s1) * (-1 - s1)) - 15) * ((t - s1)/(-1 -
s1)) + (6 - (2 * (-1 - s1) * (-1 - s1))) * ((t - s1)/(-1 -
s1)) * ((t - s1)/(-1 - s1))) + (1 - t) * ((-s2) + (1 - t) *
(2 * (-s2) + (1 - t) * (8 - 12 * (-s2) + (1 - t) * (14 *
(-s2) - 11 + (1 - t) * (4 - 5 * (-s2)))))) + ((t + s1)/(1 +
s1)) * ((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1)) * (10 -
(2 * (1 + s1) * (1 + s1)) + (2 * (2 * (1 + s1) * (1 + s1)) -
15) * ((t + s1)/(1 + s1)) + (6 - (2 * (1 + s1) * (1 + s1))) *
((t + s1)/(1 + s1)) * ((t + s1)/(1 + s1))) + (t - 1) * ((-s2) +
(t - 1) * (2 * (-s2) + (t - 1) * (t - 1) * (-2 * (-s2) -
(t - 1) * (-s2)))))^2)
}
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