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Jul 19, 2013 7:53 am
these work in isolation haven’t been able to solve a “Blend”
fn EaseTo t a =
(
res = t;
if a != 0.0 then
(
a *= 0.02;
k = 1/(2.0 - a);
if t > 1 - a then
res = -k/a * (t * (t - 2)) - (k/a - 1)
else
res = k * (2.0 * t);
)
res;
)
fn EaseFrom t a =
(
res = t;
if a != 0.0 then
(
a *= 0.02;
k = 1/(2.0 - a);
if t <= a then
res = k/a * (t * t)
else
res = k * (2.0 * t) - k*a
)
res;
)
the tcb funtion then becomes
fn tcb timev key0 key1 m0 m1 =
(
local h1, h2, h3, h4;
local t = (timev - key0.time) as float / (key1.time - key0.time) as float;
t = easeFrom t (key0.easeFrom);
--t = easeTo t (key1.easeTo);
hermite t &h1 &h2 &h3 &h4;
h1 * key0.value + h2 * key1.value + h3 * m0 + h4 * m1;
)
I can get it to work if easeIn or easeFrom is set but not both :hmm:
Jul 19, 2013 7:53 am
it’s not pretty but it works… after a fashion, going to lie down now :surprised
fn lerp x y s = (x + s * (y - x))
fn cp p = (p * 0.04 - 1.0)
fn EaseFromTo t easefrom easeto =
(
local res = t;
local s = (easefrom + easeto);
if s != 0 then
(
if s > 1.0 then
(
easefrom /= s;
easeto /= s;
)
local k = 1.0/(2.0 - easefrom - easeto);
if t < easefrom then
res = k/easefrom * t * t;
else if t > 1.0 - easeto then
res = 1.0 - k/easeto * (t * (t - 2.0) + 1.0);
else
res = k * (2.0 * t - easefrom);
)
res;
)
-- compute the in tangent
fn GetInTangent k keyframes =
(
key = keyframes[k];
if k == 1 then
prev = keyframes[k]
else
prev = keyframes[k - 1]
if k == keyframes.count then
next = keyframes[k];
else
next = keyframes[k+1];
a = (key.value - prev.value) * (1 - (cp key.tension)) * (1 - (cp key.continuity)) * (1 + (cp key.bias));
b = (next.value - key.value) * (1 - (cp key.tension)) * (1 + (cp key.continuity)) * (1 - (cp key.bias));
t = (key.time - prev.time) as float/(next.time - prev.time) as float;
(b + a) * (lerp t 0.5 (abs (cp key.continuity)));
)
-- compute the out tangent
fn GetOutTangent k keyframes =
(
key = keyframes[k];
if k == 1 then
prev = keyframes[k]
else
prev = keyframes[k - 1]
if k == keyframes.count then
next = keyframes[k];
else
next = keyframes[k+1];
a = (key.value - prev.value) * (1 - (cp key.tension)) * (1 + (cp key.continuity)) * (1 + (cp key.bias));
b = (next.value - key.value) * (1 - (cp key.tension)) * (1 - (cp key.continuity)) * (1 - (cp key.bias));
t = (next.time - key.time) as float/(next.time - prev.time) as float;
(b + a) * (lerp t 0.5 (abs (cp key.continuity)));
)
fn hermite t &h1 &h2 &h3 &h4 =
(
local t2, t3;
t2 = t * t;
t3 = t * t2;
h2 = 3.0 * t2 - t3 - t3;
h1 = 1.0 - h2;
h4 = t3 - t2;
h3 = h4 - t2 + t;
)
fn tcb timev key0 key1 m0 m1 =
(
local h1, h2, h3, h4;
local t = (timev - key0.time) as float / (key1.time - key0.time) as float;
t = EaseFromTo t (key0.easeFrom * 0.02) (key1.easeTo * 0.02);
hermite t &h1 &h2 &h3 &h4;
h1 * key0.value + h2 * key1.value + h3 * m0 + h4 * m1;
)
fn MakeTCBSpline tnode = if tnode != undefined and classof tnode.position.controller == tcb_position do
(
keys = tnode.position.controller.keys;
if keys.count >= 2 then
(
sp = splineshape();
sp.pivot = keys[1].value;
addNewSpline sp;
-- create the first knot
addKnot sp 1 #corner #line keys[1].value
-- loop over the keys
for k = 1 to keys.count - 1 do
(
start_key = k;
end_key = k + 1;
-- create the segment in and out tangents
otan = GetOutTangent start_key keys
itan = GetInTangent end_key keys
-- handle the end conditions
if start_key == 1 then otan = otan * 1.5 - itan * 0.5;
if end_key == keys.count then itan = itan * 1.5 - otan * 0.5;
-- create the knots
for f = keys[start_key].time to keys[end_key].time do
(
if f != keys[start_key].time then
addKnot sp 1 #corner #line (tcb f keys[start_key] keys[end_key] otan itan);
)
)
updateShape sp;
sp.vertexTicks = on
)
)
(
clearlistener()
MakeTCBSpline $
)
Jul 19, 2013 7:53 am
Appears to be a cubic-spline or a B-spline curve (according to my MathCAD curve fit).
Jul 19, 2013 7:53 am
thanks for the help, found a solution though not b-spline or cubic, linear if x < ease otherwise quadratic.
Jul 19, 2013 7:53 am
had to fix a couple of issues with start and end keys when tension, cont and bias != 0
fn lerp x y s = (x + s * (y - x))
fn cp p = (p * 0.04 - 1.0)
fn EaseFromTo t easefrom easeto =
(
local result = t;
local span = (easefrom + easeto);
if span != 0 then
(
if span > 1.0 then
(
easefrom /= span;
easeto /= span;
)
local c = 1.0/(2.0 - easefrom - easeto);
if t < easefrom then
result = c/easefrom * t * t;
else if t > 1.0 - easeto then
result = 1.0 - c/easeto * (t * (t - 2.0) + 1.0);
else
result = c * (2.0 * t - easefrom);
)
result;
)
fn GetInTangent k keyframes =
(
key = keyframes[k];
local continuity = cp key.continuity;
if k == 1 then
prev = keyframes[k]
else
prev = keyframes[k - 1]
if k == keyframes.count then
(
continuity = 0.0;
next = keyframes[k];
)
else
next = keyframes[k+1];
if k == keyframes.count then
(
a = (key.value - prev.value) * (1 - (cp key.tension));
b = (next.value - key.value) * (1 - (cp key.tension));
)
else
(
a = (key.value - prev.value) * (1 - (cp key.tension)) * (1 - continuity) * (1 + (cp key.bias));
b = (next.value - key.value) * (1 - (cp key.tension)) * (1 + continuity) * (1 - (cp key.bias));
)
t = (key.time - prev.time) as float/(next.time - prev.time) as float;
(b + a) * (lerp t 0.5 (abs continuity));
)
fn GetOutTangent k keyframes =
(
key = keyframes[k];
local continuity = cp key.continuity;
if k == 1 then
(
prev = keyframes[k];
continuity = 0.0;
)
else
prev = keyframes[k - 1]
if k == keyframes.count then
next = keyframes[k];
else
next = keyframes[k+1];
if k == 1 then
(
a = (key.value - prev.value) * (1 - (cp key.tension));
b = (next.value - key.value) * (1 - (cp key.tension));
)
else
(
a = (key.value - prev.value) * (1 - (cp key.tension)) * (1 + continuity) * (1 + (cp key.bias));
b = (next.value - key.value) * (1 - (cp key.tension)) * (1 - continuity) * (1 - (cp key.bias));
)
t = (next.time - key.time) as float/(next.time - prev.time) as float;
(b + a) * (lerp t 0.5 (abs continuity));
)
fn tcb timev key0 key1 m0 m1 =
(
local h1, h2, h3, h4, t2, t3;
-- get the segement time in 0-1 range
local t = (timev - key0.time) as float / (key1.time - key0.time) as float;
-- handle the time easefrom and easeto
t = EaseFromTo t (key0.easeFrom * 0.02) (key1.easeTo * 0.02);
print t
-- compute the hermite spline params
t2 = t * t;
t3 = t * t2;
h2 = 3.0 * t2 - t3 - t3;
h1 = 1.0 - h2;
h4 = t3 - t2;
h3 = h4 - t2 + t;
-- interpolate the position
h1 * key0.value + h2 * key1.value + h3 * m0 + h4 * m1;
)
fn MakeTCBSpline tnode = if tnode != undefined and classof tnode.position.controller == tcb_position do
(
keys = tnode.position.controller.keys;
if keys.count >= 2 then
(
sp = splineshape();
sp.pivot = keys[1].value;
addNewSpline sp;
-- create the first knot
addKnot sp 1 #corner #line keys[1].value
-- loop over the keys
for k = 1 to keys.count - 1 do
(
start_key = k;
end_key = k + 1;
-- create the segment in and out tangents
otan = GetOutTangent start_key keys
itan = GetInTangent end_key keys
-- handle the end conditions
if start_key == 1 then otan = otan * 1.5 - itan * (1 - (cp keys[1].tension)) * 0.5;
if end_key == keys.count then itan = itan * 1.5 - otan * (1 - (cp keys[keys.count].tension)) * 0.5;
-- create the knots
for f = keys[start_key].time to keys[end_key].time do
(
if f != keys[start_key].time then
addKnot sp 1 #corner #line (tcb f keys[start_key] keys[end_key] otan itan);
)
)
updateShape sp;
sp.vertexTicks = on
)
)
(
clearlistener()
MakeTCBSpline $
)
Jul 19, 2013 7:53 am
would be an interesting challenge to repeat the trick for the Position Bezier Controller.
Jul 19, 2013 7:53 am
what do you want to repeat? in-out tangents? i have a post on this forum about how to convert a curvecontrol curve to the bezier float controller
Jul 19, 2013 7:53 am
reverse engineer the maths need to generate bezier curve of a bezier position controller based on the key frame data or in other words bezier position controller to spline without using trajectory convert to functionality.
Jul 19, 2013 7:53 am
the solution for the bezier controller makes the TCB look like a walk in the park ! a real brain scrambler though very elegant.
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