CS430 Computer Graphics

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CS430 Computer Graphics

• Vectors Part II
• Application of Linear Combination

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Topics

• Lerp and Tweening
• Double Buffering
• Quadratic and Cubic Tweening

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Lerp and Tween

• Linear interpolation (lerp) of two points P
  A(1 - t) Bt A (B A)t
• Lerp affine combination of A and B
• P tween at t of points A and B
• lerp(a, b, t) returns the fraction t of the way
  from a to b
• float lerp(float a, float b, float t)
• return a (b a) t

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Tweening for Animation

• Morphing
• Interpolation between corresponding vertices of
  two polylines
• Fig 4.22 and 4.24 interpolation
• Fig 4.25 interpolation and extrapolation

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Tweening for Animation
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Tweening for Animation

• Generation of key frames
• Compute a smooth path to move the camera between
  key frames

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Tweening Routines - Tween

• Tween returns the tween at t of two points A and
  B
• Point2 CanvasTween(Point2 A, Point2 B, float t)
• // code of Tween is similar to lerp

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Tweening Routines - drawTween

• drawTween draws the tween polyline at t of two
  polylines A and B of n vertices
• void CanvasdrawTween(Point2 A, Point2 B,
  int n, float t)
• Point2 P Tween( A0, B0, t)
• moveTo(P)
• for (int i1 iltn i)
• P Tween( Ai, Bi, t)
• lineTo(P)

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Tweening Routines - drawAll

• drawAll draws all the tween polylines of two
  polylines A and B of n vertices on canvas cvs
• void drawAll(Point2 A, Point2 B, int n)
• for (float t0.0f tlt1.0 t 0.01f)
• glClear(GL_COLOR_BUFFER_BIT)
• cvs.drawTween( A, B, n, t)
• glutSwapBuffers()

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Double Buffering

• To generate an animation we can erase the current
  picture and then draw a new picture
• Problem Process of drawing new picture could be
  seen ? bad visual effect
• Solution double buffering
• Draw the new picture in an off-screen buffer and
  then display it by swapping the on-screen and
  off-screen buffers

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Double Buffering in OpenGL

• Initializing display mode
• glutInitDisplayMode(GLUT_DOUBLEGLUT_RGB)
• Swap buffers when a new picture ready
• glutSwapBuffers()

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Quadratic and Cubic Tweening

• Quadratic tweening
• 1 ((1 t) t)2 (1 t)2 2(1 t) t 2
• Bezier Curve for 3 points A, B, and C
• P (1 - t)2A 2t (1 t)B t 2C
• Cubic tweening
• 1 ((1-t)t)3(1-t)3 3(1-t)2t 3(1-t)t 2 t
  3
• Cubic interpolation between 4 points A, B, C, and
  D
• P (1-t)3A 3(1-t)2t B 3(1-t)t 2C t 3D

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Quadratic and Cubic Tweening
P(t)
P(1)
P(t)
P(0)