Unit5: More Collisions Mike Chantler, 31/8/2008 See Peters - - PDF document

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Unit5: More Collisions Mike Chantler, 31/8/2008 See Peters - - PDF document

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Unit 5: More Collisions 3D Modelling & Animation Module F21MA Unit5: More Collisions Mike Chantler, 31/8/2008 See Peters ActionScript 3.0 Animation Unit contents Detecting collisions Springing off a fixed ball

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Unit 5: More Collisions 1

Unit5: More Collisions

Mike Chantler, 31/8/2008 See Peters “ActionScript 3.0 Animation” 3D Modelling & Animation Module F21MA

Unit contents

  • Detecting collisions
  • Springing off a fixed ball
  • Billiard Ball Physics
  • 2D Billiard Ball Physics
  • Reference: Peters "Foundation Actionscript 3.0 Animation: Making

Things Move!"

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Unit 5: More Collisions 2

Detecting collisions

3D Modelling & Animation Module F21MA

Collisions between two objects

  • Flash’s ‘hit test’
  • Distance based
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Unit 5: More Collisions 3

Flash’s Hit Test

  • Based on bounding boxes

if(blueBall.hitTestObject(blackBall)) {…….

Perform hitTest in event handler for Event.ENTER_FRAME

Distance Based

d=sqrt( (x1-x2)2 + (y1-y2)2 ) limit2 = (r1 + r2)2 if (x1-x2)2 + (y1-y2)2 < limit2 { …..

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Unit 5: More Collisions 4

Springing off a fixed ball

3D Modelling & Animation Module F21MA

Springing

ball 1 ball 2

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Unit 5: More Collisions 5

Detect onset of Springing

dmin = r1 + r2

d = Math.sqrt( (x1-x2)2 + (y1-y2)2 )

if (d < dmin) { …. }

(x1, y1) (x2, y2)

Calculate Springing Point

dmin = r1 + r2 θ = Math.atan2((y2-y1), (x2-x1))

tx = x1 + dmin * Math.cos(θ) ty = y1 + dmin * Math.sin(θ) t = (tx, ty)

θ

(x1, y1) (x2, y2)

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Unit 5: More Collisions 6

Calculate Springing Point

t = (tx, ty)

Calculate acceleration ball 2

t = (tx, ty) ax2 = (tx – x2) * cspring ay2 = (ty – y2) * cspring (x2, y2)

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Unit 5: More Collisions 7

Calculate new ball 2 position

t = (tx, ty) vx2 += ax2; x2 += vx2 vy2 etc. (x2, y2)

Until Spring Stops

t = (tx, ty) (x2, y2)

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Unit 5: More Collisions 8

Calculate new position as before

vx2 = (tx – x2) * cspring vy2 = (ty – y2) * cspring (x2, y2)

Example

  • See bubble.as in ch09 of Peters’ download

– http://www.friendsofed.com/downloads/1590597 915/FoundationAS3Animation.zip

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Unit 5: More Collisions 9

Note

Blue ball remains stationary. To calculate movement in blue ball we need momentum/energy conservation rules [see Peters].

Billiard Ball Physics

3D Modelling & Animation Module F21MA

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Unit 5: More Collisions 10

Basic Equations

  • Momentum

p = m * v (mass * velocity)

(& note that p is a vector)

  • Conservation of Momentum

Total p before collision = total p after m0*v0 + m1*v1 = m0*v0final + m1*v1final

b0 b1 b0 b1

Basic Equations

  • Kenetic energy

KE = ½ * m * v 2

  • Conservation of Energy

Total KE collision = KE after m0*v0

2 + m1*v1 2 = m0*v0final2 + m1*v1final2

b0 b1 b0 b1

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Unit 5: More Collisions 11

Basic Equations

  • Hence

v0final = v1final = (m0 - m1)*v0 + 2*m1*v1 m0+ m1 (m1 – m0)*v1 + 2*m0*v0 m0+ m1

b0 b1 b0 b1

Implementation

  • Simple to implement in 1 dimension

v0final = v1final = (m0 - m1)*v0 + 2*m1*v1 m0+ m1 (m1 – m0)*v1 + 2*m0*v0 m0+ m1

b0 b1

y-axis

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Unit 5: More Collisions 12

Implementation

b0 b1

y-axis

  • See Billiard2.as and Ball.as in ch11 of

Peters’ download

– http://www.friendsofed.com /downloads /1590597915 /FoundationAS3Animation.zip

Sanity check

  • What if m0 >> m1?

v0final = v1final = (m0 - m1)*v0 + 2*m1*v1 m0+ m1 (m1 – m0)*v1 + 2*m0*v0 m0+ m1

b0

b1

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Unit 5: More Collisions 13

Sanity check

  • What if m0 >> m1?

v0final = v1final = v1final = (m0)*v0 m0 (– m0)*v1 + 2*m0*v0 m0

b0

b1

b0

b1

–v1 + 2*v0

2D Billiard Ball Physics

3D Modelling & Animation Module F21MA

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Unit 5: More Collisions 14

The 2D case At point of collision

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Unit 5: More Collisions 15

Rotate axis of collision to x-axis Rotate axis of collision to x-axis

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Unit 5: More Collisions 16

Rotate axis of collision to x-axis

Resolve velocities into x & y components

vx = vsin θ vy = vcos θ

θ

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Unit 5: More Collisions 17

Remember the Coord-system

θ (x1,y1)

x y

x1 = rsinθ y1 = rcosθ r

  • In the

second quadrant x1 is negative and y1 is positive

Resolve velocities into x & y components for other ball

vx = vsin θ vy = vcos θ

θ

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Unit 5: More Collisions 18

Consider only x components

Apply 1D equations to x final components

v0final = v1final = (m0 - m1)*v0 + 2*m1*v1 m0+ m1 (m1 – m0)*v1 + 2*m0*v0 m0+ m1

b0 b1

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Result: final x components

Add original y components back in

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Rotate everything back Implementation

  • See Billiard4.as in ch11 of Peters’ download

– http://www.friendsofed.com /downloads /1590597915 /FoundationAS3Animation.zip

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Unit 5: More Collisions 21

Notes on Implementation

  • Billiard4.as uses flash.geom.Point class

The Point object represents a location (x, y) e.g.

import flash.geom.Point; private var point2:Point = new Point(6, 8);

Its not all that great for us – but its what I’d build upon to create a point class for representing positions, velocities, and accelerations. I’d add better polar, rotation and other transformation functions.

Lab: ex5.1

3D Modelling & Animation Module F21MA

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Unit 5: More Collisions 22

Create a Test

  • For a stationary ball and a draggable ball

if(blueBall.hitTestObject(blackBall)) {…….

Perform hitTest in event handler for Event.ENTER_FRAME

Lab: ex5.2

3D Modelling & Animation Module F21MA

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Unit 5: More Collisions 23

Implement spring based collisions

t = (tx, ty) ax2 = (tx – x2) * cspring ay2 = (ty – y2) * cspring (x2, y2)

End

3D Modelling & Animation Module F21MA