I made a small mistake at the "current angle" (it should be -0.2ish radians instead of -pi/4), which makes the angle difference close to a semicircle. But still, if you add that, you end up with a vector pointing up and backwards... (If you subtract, you end up just heading back left...)
Maybe I'm just not interpreting what you mean by the "twist" correctly? (Even when I 'visually' do it to your picture, I get the same result...) Am I supposed to be finding the angle between the velocity vectors, or the angle between the (position - intersection point) vectors? (We might want to work things out off-list, unless anyone would like to see those details.) Celi . On Fri, Feb 5, 2010 at 10:22 PM, Nexii Malthus <nex...@googlemail.com>wrote: > Ah, thanks Celierra. 3 planes, yes that makes a lot more sense. > > Hmm, trying to step through your calculations. I think you have to subtract > the angle difference rather than add it on. > I just tried visually going through your calcs and it seems to hit right on > your perfect value p3. > > http://i48.tinypic.com/15x2wz8.png > > - Nexii > > > > On Sat, Feb 6, 2010 at 1:28 AM, Celierra Darling <celie...@gmail.com> > wrote: > > I'm not sure about this -- I tried this with a free-flight parabola and > got > > a nonsense value out. Calculations attached at the end. > > What is the significance of the "anchor"? It looks like you're trying to > > estimate the center of the path's curvature? If you were doing that, you > > want to intersect using the lines through p and *perpendicular* to v (in > > 2D), not intersect the lines created by v. In 3D, I think you'd want to > > intersect 3 planes, the two planes through p perpendicular to their > > respective v and also the plane that contains both points. > > I'm not sure how to extend that to handle torques on the object.... > > Have you tried estimating a = (v1 - v2)/t, and extrapolating using that > > (p_next = p_cur + v_cur*dt + 1/2*a*dt^2)? It would also extend to > torques > > and angular velocity using the analogous equation. (I'm sure you could > even > > fit a line or spline to multiple previous values of v to get something > even > > higher-order, if you wanted, though with diminishing returns.) > > > > Celi > > The aforementioned calculation: > > > > dt = 0.1 > > a = g = [0,-2] > > initial position and velocity: > > p1 = [0, 0] > > v1 = [1, 0] > > next position and velocity > > p2 = [0.1, -0.01] > > v2 = [1, -0.2] > > perfect value: p3 = [0.2, -0.04] > > lines are (p1 + s*v1) and (p2 + t*v2) > > intersect at s = 0.05, t = -0.05, position = [0.05, 0] > > angle change = clockwise 3pi/4 (radians) > > current angle = -pi/4 > > angle after "twist" = pi/2 (upwards!?) > > (it just gets worse from here - you estimate a distance upwards, and the > > step forward using the current velocity doesn't get you back to y=0.) > >
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