Interactive spacetime constraints: wiggly splines

• US 20060192783A1
• Filed: 01/26/2006
• Published: 08/31/2006
• Est. Priority Date: 01/26/2005
• Status: Active Grant

• Current Assignee: Pixar (The Walt Disney Company)
• Original Assignee: Pixar (The Walt Disney Company)
• Inventors: Anderson, John, Kass, Michael
• Granted Patent: US 7,483,030 B2
• Time in Patent Office: Days
• US Class Current: 345/473
• CPC Class Codes: G06T 11/203 Drawing of straight lines or curves
• CPC Class Codes: G06T 13/80 2D [Two Dimensional] animation, e.g. using sprites
• CPC Class Codes: G06T 2213/12 Rule based animation

Abstract

Animation techniques for producing physically-realistic animation while providing the interactivity and control desired by animators. Techniques are provided specifying animation for motion problems that give rise to quadratic optimization functions solvable with linear systems of equations. The resultant splines generalize traditional splines to encompass oscillatory solutions. These problems can be solved at full frame rates, giving animators a keyframe animation tool. Such a formulation is able to address a wide range of oscillatory phenomena while retaining the interactive performance and predictability of traditional splines. The splines may be complex-valued.

Claims

1. In a computer-implemented animation system, a method for animating an object, the method comprising:

receiving a set of one or more constraints;

determining a set of values for a first parameter associated with the object over a plurality of time points using a set of linear equations, the set of linear equations providing a solution to a function specifying oscillatory motion; and

generating an animation curve for the parameter based upon the determined set of values.

2. The method of claim 1 wherein the function models a mass-spring oscillator.

3. The method of claim 1 further comprising:

receiving information identifying a set of behavior characteristics; and

wherein the set of values approximates or interpolates the set of constraints and is based upon the set of behavior characteristics.

4. The method of claim 3 wherein:

the set of constraints comprises an interpolation constraint and a tangent constraint; and

the set of behavior characteristics comprises a damping factor and a resonance value.

5. The method of claim 3 further comprising:

displaying the animation curve for the first parameter; and

displaying the set of constraints.

6. The method of claim 5 further comprising:

receiving information indicating a change in at least one constraint in the set of constraints; and

generating an animation curve for the first parameter that interpolates or approximates the changed set of constraints.

7. The method of claim 6 wherein generating the animation curve that interpolates or approximates the changed set of constraints is performed at an interactive rate of 30 frames per second or less.

8. The method of claim 1 wherein the set of values comprises at least a first value having a real part and a non-zero imaginary part.

9. The method of claim 8 further comprising:

generating an animation curve for a second parameter associated with the object using the animation curve generated for the first parameter and the non-zero imaginary part.

10. In a computer-implemented animation system, a method for animating an object, the method comprising:

generating an animation curve for a first parameter associated with the object, the animation curve generated based upon a set of values calculated for the first parameter over time, the set of values comprising a first value having a real part and a non-zero imaginary part; and

controlling animation of the first parameter using the animation curve.

11. The method of claim 10 wherein the non-zero imaginary part identifies a phase angle.

12. The method of claim 10 further comprising:

generating an animation curve for a second parameter associated with the object using the animation curve generated for the first parameter and the non-zero imaginary part.

13. The method of claim 12 wherein:

the non-zero imaginary part indicates a phase value; and

the animation curve for the second parameter is phase-shifted from the animation curve for the first parameter by the phase value.

14. The method of claim 12 wherein:

the non-zero imaginary part indicates a phase value; and

motion of the second parameter is phase-shifted from motion of the first parameter.

15. The method of claim 10 wherein generating the animation curve for the first parameter comprises:

determining a set values for the first parameter over a plurality of time points using a set of linear equations, the set of linear equations providing a solution to a function specifying motion.

16. The method of claim 15 wherein the function represents oscillatory motion.

17. The method of claim 15 wherein the function models a mass-spring oscillator.

18. The method of claim 10 further comprising:

receiving information identifying a set of behavior characteristics;

receiving information identifying a set of constraints; and

wherein generating the animation curve for the first parameter comprises generating an animation curve that approximates or interpolates the set of constraints and is based upon the set of behavior characteristics.

19. The method of claim 18 wherein:

the set of constraints comprises an interpolation constraint and a tangent constraint; and

the set of behavior characteristics comprises a damping factor and a resonance value.

20. The method of claim 18 further comprising:

displaying the animation curve for the first parameter; and

displaying a representation of the set of constraints.

21. The method of claim 20 further comprising:

receiving information indicating a change in at least one constraint in the set of constraints; and

generating an animation curve for the first parameter that interpolates or approximates the changed set of constraints.

22. The method of claim 21 wherein generating the animation curve that interpolates or approximates the changed set of constraints is performed at an interactive rate of 30 frames per second or less.

23. A system for performing animation, the system comprising:

a processing module configured to;

receive a set of one or more constraints;

determine a set of values for a first parameter associated with the object over a plurality of time points using a set of linear equations, the set of linear equations providing a solution to a function specifying oscillatory motion; and

generate an animation curve for the parameter based upon the determined set of values; and

a display module configured to output the animation curve.

24. The system of claim 23 wherein the function models a mass-spring oscillator.

25. The system of claim 23 wherein the processing module is configured to:

receive information identifying a set of behavior characteristics, the set of behavior characteristics comprising at least one of a damping factor or a resonance value;

wherein the set of values approximates or interpolates the set of constraints and is based upon the set of behavior characteristics;

cause the display module to display the animation curve for the first parameter;

cause the display module to display the set of constraints;

receive information indicating a change in at least one constraint in the set of constraints; and

generate an animation curve for the first parameter that interpolates or approximates the changed set of constraints.

26. The system of claim 25 wherein generating the animation curve that interpolates or approximates the changed set of constraints is performed at an interactive rate of 30 frames per second or less.

27. The system of claim 23 wherein the set of values comprises at least a first value having a real part and a non-zero imaginary part.

28. The system of claim 27 wherein the processing module is configured to generate an animation curve for a second parameter associated with the object using the animation curve generated for the first parameter and the non-zero imaginary part.

29. A system for performing animation, the system comprising:

a processing module configured to;

generate an animation curve for a first parameter associated with the object, the animation curve generated based upon a set of values calculated for the first parameter over time, the set of values comprising a first value having a real part and a non-zero imaginary part; and

enable controlling animation of the first parameter using the animation curve; and

a display module configured to display the animation curve.

30. The system of claim 29 wherein the non-zero imaginary part identifies a phase angle.

31. The system of claim 29 wherein the processing module is configured to:

generate an animation curve for a second parameter associated with the object using the animation curve generated for the first parameter and the non-zero imaginary part.

32. The system of claim 29 wherein the processing module is configured to generate the animation curve for the first parameter by:

determining a set values for the first parameter over a plurality of time points using a set of linear equations, the set of linear equations providing a solution to a function specifying motion.

33. The system of claim 32 wherein the function represents oscillatory motion.

34. The system of claim 29 wherein the processing module is configured to:

receive information identifying a set of behavior characteristics;

receive information identifying a set of constraints;

generate an animation curve that approximates or interpolates the set of constraints and is based upon the set of behavior characteristics;

cause the display module to display the animation curve for the first parameter and a representation of the set of constraints;

receive information indicating a change in at least one constraint in the set of constraints; and

generate an animation curve for the first parameter that interpolates or approximates the changed set of constraints.

35. The system of claim 34 wherein the processing module generates the animation curve that interpolates or approximates the changed set of constraints at an interactive rate of 30 frames per second or less.