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author | Karl Berry <karl@freefriends.org> | 2010-07-11 22:39:53 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2010-07-11 22:39:53 +0000 |
commit | 4e8485b0ddecb55f72929dd6233f254a1e7bf5b0 (patch) | |
tree | 354324ee6f54d46053b3ce88fe9dc4acf8e2ed81 /Build/source/utils/asymptote/doc/extra/intro.asy | |
parent | 713bb91ad0467fb3b12acad03cae2fa105ed2caa (diff) |
asy 2.02
git-svn-id: svn://tug.org/texlive/trunk@19378 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/utils/asymptote/doc/extra/intro.asy')
-rw-r--r-- | Build/source/utils/asymptote/doc/extra/intro.asy | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/Build/source/utils/asymptote/doc/extra/intro.asy b/Build/source/utils/asymptote/doc/extra/intro.asy index 20b03c578dc..5d7ce12b184 100644 --- a/Build/source/utils/asymptote/doc/extra/intro.asy +++ b/Build/source/utils/asymptote/doc/extra/intro.asy @@ -352,13 +352,9 @@ item("Having prescribed outgoing and incoming path directions $e^{i\theta}$ at node~$z_0$ and $e^{i\phi}$ at node $z_1$ relative to the vector $z_1-z_0$, the control points are determined as:"); -skip(-3); - equations("u&=&z_0+e^{i\theta}(z_1-z_0)f(\theta,-\phi),\nonumber\\ v&=&z_1-e^{i\phi}(z_1-z_0)f(-\phi,\theta),"); -skip(-3); - remark("where the relative distance function $f(\theta,\phi)$ is given by Hobby [1986]."); asyfigure("Hobbycontrol","height=9cm"); @@ -376,9 +372,13 @@ equation("\displaystyle x(t)=\sum_{k=0}^3 B_k(t) P_k, \qquad t\in [0,1]."); item("The resulting curve is also a B\'ezier curve:"); +skip(-2); + equations("x'_i(t)&=&\sum_{k=0}^3 B_k(t) A_{ij}(P_k)_j+C_i\nonumber\\ &=&\sum_{k=0}^3 B_k(t) P'_k,"); +skip(-2); + remark("where $P'_k$ is the transformed $k^{\rm th}$ control point, noting $\displaystyle\sum_{k=0}^3 B_k(t)=1.$"); } |