Revisions to Animate point going around a triangle

added 1 character in body

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edited Feb 17, 2015 at 2:55

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94

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animation animation2

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animation

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animation2

animation

Source Link

edited Feb 17, 2015 at 1:02

DavidC

16.8k
1
42
94

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animator animation

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animator

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animation

added 113 characters in body

Source Link

edited Feb 16, 2015 at 22:15

DavidC

16.8k
1
42
94

Using `RegionNearest`

ImagineThis approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animator

Using `RegionNearest`

Imagine the triangle as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animator

Using `RegionNearest`

This approach should work regardless of whether the triangle is filled or not. Here, we will represent the triangle unfilled, i.e. as a one-dimensional region, r1, a line, embedded in a plane.

r1 = Line[{{0, 0}, {3, 1}, {2, 0}, {0, 0}}];
RegionDimension[r1]
RegionEmbeddingDimension[r1]

1
2

Get the radius of a circle, with the triangle centroid as center, that intersects the farthest vertex of the triangle.

c = RegionCentroid[r1];  (* the gray point *)
radius = Max[EuclideanDistance[c, #] & /@ {{0, 0}, {3, 1}, {2, 0}}];

Animate a black point going around the circle.

And display a (red) point on the triangle that is currently nearest to the black point on the circle.

Animator[Dynamic[n], {0, N[2 Pi], .01}]
Graphics[{r1, AbsolutePointSize[10],
  Gray, Point[c],
  Black, Dynamic@ Point[d = radius {Cos[n], Sin[n]} + c],
  {Red, Dynamic@Point[RegionNearest[r1, d]]},
  {Dashed, Circle[c, radius]}}]

animator

added 2 characters in body

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edited Jan 25, 2015 at 0:34

Mr.Wizard

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complete rewrite

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edited Jan 24, 2015 at 23:17

DavidC

16.8k
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42
94

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added 326 characters in body

Source Link

edited Jan 24, 2015 at 22:34

DavidC

16.8k
1
42
94

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Source Link

created Jan 24, 2015 at 22:13

DavidC

16.8k
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42
94

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Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Return to Answer

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using RegionNearest

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`

Using `RegionNearest`