Animating wave motion in water
19
$begingroup$
Further to this question I found on MSE, I tried to replicate
from here
this is as far as I got:
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
tab = With[{a = #},
Flatten[Table[
Table[fun[a, 90 + 15 n, 1 - .15 m, -1 + .5 n, -.35 m], {m, 0,
10}], {n, 0, 24}], 1]] & /@ Range[1, 360, 15];
Module[{t, x, y, fun, xf, yf, a}, x = -.5; y = 1;
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
xf[t_, a_, b_] := a t - b Sin[t]; yf[t_, a_, b_] := a - b Cos[t];
Animate[
Show[
Graphics[
{PointSize[.01], tab[[a]]},
PlotRange -> {{-1 - x, 10 + x}, {-1 - y, 1}}
],
ParametricPlot[
{(Pi/2) xf[t + 2 Pi a/24, 1.25, .6] - 4 Pi a/24 - Pi^2 + .05,
2.05 - 1.65 yf[t + 2 Pi a/24, 1.25, .6]},
{t, -4 Pi, 4 Pi}, Axes -> False
]
],
{a, 1, 24, 1}, ControlPlacement -> Top, AnimationRate -> 5,
AnimationDirection -> Backward
]
]
which is not very efficient (I'm sure Part could be applied more efficiently), and despite various tweeks, I couldn't quite manage to get the cycloid to line up with the points.
What is a better way to approach this?
performance-tuning animation
edited 2 days ago
Kuba♦
107k12210530
asked 2 days ago
martinmartin
4,01821249
$endgroup$
add a comment |
19
$begingroup$
Further to this question I found on MSE, I tried to replicate
from here
this is as far as I got:
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
tab = With[{a = #},
Flatten[Table[
Table[fun[a, 90 + 15 n, 1 - .15 m, -1 + .5 n, -.35 m], {m, 0,
10}], {n, 0, 24}], 1]] & /@ Range[1, 360, 15];
Module[{t, x, y, fun, xf, yf, a}, x = -.5; y = 1;
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
xf[t_, a_, b_] := a t - b Sin[t]; yf[t_, a_, b_] := a - b Cos[t];
Animate[
Show[
Graphics[
{PointSize[.01], tab[[a]]},
PlotRange -> {{-1 - x, 10 + x}, {-1 - y, 1}}
],
ParametricPlot[
{(Pi/2) xf[t + 2 Pi a/24, 1.25, .6] - 4 Pi a/24 - Pi^2 + .05,
2.05 - 1.65 yf[t + 2 Pi a/24, 1.25, .6]},
{t, -4 Pi, 4 Pi}, Axes -> False
]
],
{a, 1, 24, 1}, ControlPlacement -> Top, AnimationRate -> 5,
AnimationDirection -> Backward
]
]
which is not very efficient (I'm sure Part could be applied more efficiently), and despite various tweeks, I couldn't quite manage to get the cycloid to line up with the points.
What is a better way to approach this?
performance-tuning animation
edited 2 days ago
Kuba♦
107k12210530
asked 2 days ago
martinmartin
4,01821249
$endgroup$
$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago
add a comment |
19
19
19
8
$begingroup$
Further to this question I found on MSE, I tried to replicate
from here
this is as far as I got:
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
tab = With[{a = #},
Flatten[Table[
Table[fun[a, 90 + 15 n, 1 - .15 m, -1 + .5 n, -.35 m], {m, 0,
10}], {n, 0, 24}], 1]] & /@ Range[1, 360, 15];
Module[{t, x, y, fun, xf, yf, a}, x = -.5; y = 1;
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
xf[t_, a_, b_] := a t - b Sin[t]; yf[t_, a_, b_] := a - b Cos[t];
Animate[
Show[
Graphics[
{PointSize[.01], tab[[a]]},
PlotRange -> {{-1 - x, 10 + x}, {-1 - y, 1}}
],
ParametricPlot[
{(Pi/2) xf[t + 2 Pi a/24, 1.25, .6] - 4 Pi a/24 - Pi^2 + .05,
2.05 - 1.65 yf[t + 2 Pi a/24, 1.25, .6]},
{t, -4 Pi, 4 Pi}, Axes -> False
]
],
{a, 1, 24, 1}, ControlPlacement -> Top, AnimationRate -> 5,
AnimationDirection -> Backward
]
]
which is not very efficient (I'm sure Part could be applied more efficiently), and despite various tweeks, I couldn't quite manage to get the cycloid to line up with the points.
What is a better way to approach this?
performance-tuning animation
edited 2 days ago
Kuba♦
107k12210530
asked 2 days ago
martinmartin
4,01821249
$endgroup$
Further to this question I found on MSE, I tried to replicate
from here
this is as far as I got:
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
tab = With[{a = #},
Flatten[Table[
Table[fun[a, 90 + 15 n, 1 - .15 m, -1 + .5 n, -.35 m], {m, 0,
10}], {n, 0, 24}], 1]] & /@ Range[1, 360, 15];
Module[{t, x, y, fun, xf, yf, a}, x = -.5; y = 1;
fun[a_, b_, c_, x_, y_] :=
Point[{#[[1]] + x, #[[2]] + y} &[
Part[CirclePoints[360] c,
If[a + b == 360, 360, Mod[a + b, 360]]]]];
xf[t_, a_, b_] := a t - b Sin[t]; yf[t_, a_, b_] := a - b Cos[t];
Animate[
Show[
Graphics[
{PointSize[.01], tab[[a]]},
PlotRange -> {{-1 - x, 10 + x}, {-1 - y, 1}}
],
ParametricPlot[
{(Pi/2) xf[t + 2 Pi a/24, 1.25, .6] - 4 Pi a/24 - Pi^2 + .05,
2.05 - 1.65 yf[t + 2 Pi a/24, 1.25, .6]},
{t, -4 Pi, 4 Pi}, Axes -> False
]
],
{a, 1, 24, 1}, ControlPlacement -> Top, AnimationRate -> 5,
AnimationDirection -> Backward
]
]
which is not very efficient (I'm sure Part could be applied more efficiently), and despite various tweeks, I couldn't quite manage to get the cycloid to line up with the points.
What is a better way to approach this?
performance-tuning animation
performance-tuning animation
edited 2 days ago
Kuba♦
107k12210530
asked 2 days ago
martinmartin
4,01821249
edited 2 days ago
Kuba♦
107k12210530
asked 2 days ago
martinmartin
4,01821249
edited 2 days ago
Kuba♦
107k12210530
edited 2 days ago
Kuba♦
107k12210530
edited 2 days ago
Kuba♦
107k12210530
107k12210530
asked 2 days ago
martinmartin
4,01821249
asked 2 days ago
martinmartin
4,01821249
asked 2 days ago
martinmartin
4,01821249
4,01821249
$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago
add a comment |
$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago
$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago
$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
27
$begingroup$
DynamicModule[{t = 0, d = 5, a = .08, base, distortion, pts, r, f, n = 10},
r[y_] := .08 y^4;
f[x_] := -2 Pi Dynamic[t] + d x;
(*f does not evaluate to a number but FE will take care of that later*)
base = Array[List, n {3, 1}, {{0, Pi}, {0, 1}} ];
distortion = Array[
Function[{x, y}, r[y] {Cos @ f @ x, Sin @ f @ x}], n {3, 1}, {{0, Pi}, {0, 1}}
];
pts = base + distortion;
Row[{
Animator[Dynamic @ t, AnimationRate -> .8, AppearanceElements -> {}],
Graphics[{
LightBlue,
Polygon @ Join[ pts[[;; , -1]], {Scaled[{1, 0}], Scaled[{0, 0}]}],
Darker @ Blue, AbsolutePointSize @ 5, Point @ Catenate @ pts,
AbsolutePointSize @ 7, Orange, Thick,
Point @ pts[[15, -1]], Circle[base[[15, -1]], r @ base[[15, -1, 2]]],
Point @ pts[[15, 7]], Circle[base[[15, 7]], r @ base[[15, 7, 2]]]
},
PlotRange -> {{0 + .1, Pi - .1}, {0, 1.2}},
PlotRangePadding -> 0,
PlotRangeClipping -> True, ImageSize -> 800]
}]
]
answered 2 days ago
Kuba♦Kuba
107k12210530
$endgroup$
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
27
$begingroup$
DynamicModule[{t = 0, d = 5, a = .08, base, distortion, pts, r, f, n = 10},
r[y_] := .08 y^4;
f[x_] := -2 Pi Dynamic[t] + d x;
(*f does not evaluate to a number but FE will take care of that later*)
base = Array[List, n {3, 1}, {{0, Pi}, {0, 1}} ];
distortion = Array[
Function[{x, y}, r[y] {Cos @ f @ x, Sin @ f @ x}], n {3, 1}, {{0, Pi}, {0, 1}}
];
pts = base + distortion;
Row[{
Animator[Dynamic @ t, AnimationRate -> .8, AppearanceElements -> {}],
Graphics[{
LightBlue,
Polygon @ Join[ pts[[;; , -1]], {Scaled[{1, 0}], Scaled[{0, 0}]}],
Darker @ Blue, AbsolutePointSize @ 5, Point @ Catenate @ pts,
AbsolutePointSize @ 7, Orange, Thick,
Point @ pts[[15, -1]], Circle[base[[15, -1]], r @ base[[15, -1, 2]]],
Point @ pts[[15, 7]], Circle[base[[15, 7]], r @ base[[15, 7, 2]]]
},
PlotRange -> {{0 + .1, Pi - .1}, {0, 1.2}},
PlotRangePadding -> 0,
PlotRangeClipping -> True, ImageSize -> 800]
}]
]
answered 2 days ago
Kuba♦Kuba
107k12210530
$endgroup$
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
add a comment |
27
$begingroup$
DynamicModule[{t = 0, d = 5, a = .08, base, distortion, pts, r, f, n = 10},
r[y_] := .08 y^4;
f[x_] := -2 Pi Dynamic[t] + d x;
(*f does not evaluate to a number but FE will take care of that later*)
base = Array[List, n {3, 1}, {{0, Pi}, {0, 1}} ];
distortion = Array[
Function[{x, y}, r[y] {Cos @ f @ x, Sin @ f @ x}], n {3, 1}, {{0, Pi}, {0, 1}}
];
pts = base + distortion;
Row[{
Animator[Dynamic @ t, AnimationRate -> .8, AppearanceElements -> {}],
Graphics[{
LightBlue,
Polygon @ Join[ pts[[;; , -1]], {Scaled[{1, 0}], Scaled[{0, 0}]}],
Darker @ Blue, AbsolutePointSize @ 5, Point @ Catenate @ pts,
AbsolutePointSize @ 7, Orange, Thick,
Point @ pts[[15, -1]], Circle[base[[15, -1]], r @ base[[15, -1, 2]]],
Point @ pts[[15, 7]], Circle[base[[15, 7]], r @ base[[15, 7, 2]]]
},
PlotRange -> {{0 + .1, Pi - .1}, {0, 1.2}},
PlotRangePadding -> 0,
PlotRangeClipping -> True, ImageSize -> 800]
}]
]
answered 2 days ago
Kuba♦Kuba
107k12210530
$endgroup$
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
add a comment |
27
27
27
$begingroup$
DynamicModule[{t = 0, d = 5, a = .08, base, distortion, pts, r, f, n = 10},
r[y_] := .08 y^4;
f[x_] := -2 Pi Dynamic[t] + d x;
(*f does not evaluate to a number but FE will take care of that later*)
base = Array[List, n {3, 1}, {{0, Pi}, {0, 1}} ];
distortion = Array[
Function[{x, y}, r[y] {Cos @ f @ x, Sin @ f @ x}], n {3, 1}, {{0, Pi}, {0, 1}}
];
pts = base + distortion;
Row[{
Animator[Dynamic @ t, AnimationRate -> .8, AppearanceElements -> {}],
Graphics[{
LightBlue,
Polygon @ Join[ pts[[;; , -1]], {Scaled[{1, 0}], Scaled[{0, 0}]}],
Darker @ Blue, AbsolutePointSize @ 5, Point @ Catenate @ pts,
AbsolutePointSize @ 7, Orange, Thick,
Point @ pts[[15, -1]], Circle[base[[15, -1]], r @ base[[15, -1, 2]]],
Point @ pts[[15, 7]], Circle[base[[15, 7]], r @ base[[15, 7, 2]]]
},
PlotRange -> {{0 + .1, Pi - .1}, {0, 1.2}},
PlotRangePadding -> 0,
PlotRangeClipping -> True, ImageSize -> 800]
}]
]
answered 2 days ago
Kuba♦Kuba
107k12210530
$endgroup$
DynamicModule[{t = 0, d = 5, a = .08, base, distortion, pts, r, f, n = 10},
r[y_] := .08 y^4;
f[x_] := -2 Pi Dynamic[t] + d x;
(*f does not evaluate to a number but FE will take care of that later*)
base = Array[List, n {3, 1}, {{0, Pi}, {0, 1}} ];
distortion = Array[
Function[{x, y}, r[y] {Cos @ f @ x, Sin @ f @ x}], n {3, 1}, {{0, Pi}, {0, 1}}
];
pts = base + distortion;
Row[{
Animator[Dynamic @ t, AnimationRate -> .8, AppearanceElements -> {}],
Graphics[{
LightBlue,
Polygon @ Join[ pts[[;; , -1]], {Scaled[{1, 0}], Scaled[{0, 0}]}],
Darker @ Blue, AbsolutePointSize @ 5, Point @ Catenate @ pts,
AbsolutePointSize @ 7, Orange, Thick,
Point @ pts[[15, -1]], Circle[base[[15, -1]], r @ base[[15, -1, 2]]],
Point @ pts[[15, 7]], Circle[base[[15, 7]], r @ base[[15, 7, 2]]]
},
PlotRange -> {{0 + .1, Pi - .1}, {0, 1.2}},
PlotRangePadding -> 0,
PlotRangeClipping -> True, ImageSize -> 800]
}]
]
answered 2 days ago
Kuba♦Kuba
107k12210530
edited 2 days ago
answered 2 days ago
Kuba♦Kuba
107k12210530
answered 2 days ago
Kuba♦Kuba
107k12210530
answered 2 days ago
Kuba♦Kuba
107k12210530
107k12210530
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
add a comment |
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
thanks - a vastly better approach!
$endgroup$
– martin
2 days ago
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
$begingroup$
@martin thanks, let me know if anything is not clear.
$endgroup$
– Kuba♦
yesterday
add a comment |
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$begingroup$
See this: mathematica.stackexchange.com/questions/123127/…
$endgroup$
– LCarvalho
2 days ago