I'm trying to implement the techniques found in this paper: link A strand of hair is represented by a set of particles connected by springs. The velocity for a particular particle is calculated implicitly using the following formula:
$\boldsymbol{v}^{n+1/2}=\boldsymbol{v}^{n}+\frac{\Delta t}{2}\boldsymbol{a}(t^{n+1/2},\boldsymbol{x}^{n},\boldsymbol{v}^{n+1/2})$ The force or acceleration ( where My question is, how do you numerically calculate EDIT: open again I've tried using Newton's Method but calculating derivative the spring force is just so complicated. I'm attempting to implement the techniques found in this paper: link$\boldsymbol{a}$ in the above equation) produced by the spring between two adjacent particles is given by the following:
$\boldsymbol{F}^{n+1}=\frac{k}{l_{0}}\left((\boldsymbol{x}_{2}^{n}-\boldsymbol{x}_{1}^{n})^{\mathrm{T}}\hat{\boldsymbol{d}}^{n}-l_{0}\right)\hat{\boldsymbol{d}}^{n}+\Delta t\frac{k}{l_{0}}(\boldsymbol{v}_{2}^{n+1}-\boldsymbol{v}_{1}^{n+1})^{\mathrm{T}}\hat{\boldsymbol{d}}^{n}\hat{\boldsymbol{d}}^{n}$$\hat{d}^{n}=(x_{2}^{n}-x_{1}^{n})/\left\Vert x_{2}^{n}-x_{1}^{n}\right\Vert$$\boldsymbol{v}_{1}^{n+1}$ and $\boldsymbol{v}_{2}^{n+1}$ in order to calculate the force?
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I'm trying to implement the techniques found in this paper: link The velocity for a particular particle is calculated implicitly using the following formula: $\boldsymbol{v}^{n+1/2}=\boldsymbol{v}^{n}+\frac{\Delta t}{2}\boldsymbol{a}(t^{n+1/2},\boldsymbol{x}^{n},\boldsymbol{v}^{n+1/2})$ The force or acceleration in the above equation is given by the following:
where My question is, how do you numerically calculate EDIT: open again. |
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Post Reopened by José Figueroa-O'Farrill, Emerton, Will Jagy, Gjergji Zaimi, S. Carnahan♦
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Post Closed as "off topic" by Qiaochu Yuan, Andres Caicedo, Andy Putman, Igor Rivin, Ryan Budney
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