Principles of Animation

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Principles of Animation

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Just about every object you can create in Sketchpad can be animated. To animate an object, you can choose Display | Animate, use the Motion Controller, or create an Animation action button. Of these three methods, action buttons give you the most control of the details of motion.

The only objects you can’t animate are captions, calculations, functions, action buttons, measurements, and pictures. (Except for action buttons, each of these objects can be attached to a point, and the point can be animated.)

You can also move an object automatically by creating a Movement action button.

How Objects Move

Different objects in Sketchpad move in different ways.

An independent point moves randomly on the plane.

A point on path moves along its path. If the path is an interior (polygon, circle interior, or arc interior), the point moves along the perimeter of the interior.

For open paths (straight objects, arcs, and some point loci) default direction is bidirectional. For circles and circle interiors, it’s counter-clockwise, and for other closed paths it’s forward (based on the order of the parent objects). You can change the direction using the Motion Controller or the properties of the Animation button.

A parameter changes its value.

Any other object moves by moving its parent objects.

If you animate this triangle interior, it moves its parent objects (vertices A, B, and C). Vertex A (an independent point) moves randomly on the plane, vertex B (a point on a segment) moves bidirectionally along its path, and point C (an intersection) moves the intersecting segments, which in turn move their endpoints. Thus your ability to animate any geometric object is ultimately based on animating independent points and points constructed on paths. All other objects are animated indirectly — by animating their parents.

Except for parameters, non-geometric objects (action buttons, measurements, calculations, functions, and captions) cannot be animated (unless they are merged to a point). A parameter is like an independent point in the sense that its value, like the position of an independent point, does not depend on other objects. Sketchpad animates a parameter by changing its value.

Because independent points, points on paths, and parameters are the only objects that can be animated independently of their parents, these are the only objects that Sketchpad directly animates, and they are normally the only objects that appear in the Motion Controller’s Target pop-up menu.

Other objects can be listed as the Motion Controller target if they are selected. For example, if you select the interior of ABC, the triangle will be listed as the target. Even though the triangle is listed as the target, any motion changes you make will directly affect points A, B, and C and will affect the triangle indirectly.

Animation of an Independent Point

An independent point is animated by moving it randomly on the plane. The animation speed determines how far it’s likely to move in each random step. You cannot control the direction for an independent point. To specify the starting animation speed explicitly or to make the motion occur one time only, create an Animation button and use the Animate Properties panel.

Merge the independent point to a path if you want it to move in a specific direction.

Animation of a Point on Path

A point on path is animated by moving along its path. If the path is closed (for example, a circle, a polygon, an arc sector, or an arc segment) the animation proceeds around and around the path. If the path is a segment or an arc, the animation proceeds bidirectionally — back and forth along the path. If the path is infinite, as with a line or a ray, Sketchpad animates the point bidirectionally and tries to use the portion of the path that’s visible in the window. To specify the direction or speed explicitly or to make the point travel its path only once, create an Animation button and use the Animate Properties panel.

To designate a specific portion of a line or ray as the domain for an animating point, construct a segment collinear with the line or ray and merge the point to the segment.

Animation of a Parameter

A parameter is animated by changing its value within its domain. The default domain, direction, and speed of a parameter’s variation depends on the units of the parameter, as shown in this table.

The speed listed here is a maximum. A parameter may change more slowly if your computer is busy with many tasks.






–100 to 100 units


1 unit/sec


0° to 360°




0 to 2π


π/4 radians/sec


0 to 100 inches


1 inch/sec


0 to 100 cm


1 cm/sec


To specify the direction, domain, or speed explicitly, choose Edit | Properties | Parameter or create an Animation button and use Animate Properties.

Motion Direction

The possible directions in which you can animate an object depends on the kind of object. When you start an animation using Animate or the Motion Controller, Sketchpad uses the most common direction for the objects you animate. To access more advanced direction choices, create an Animation button.

A point on a path can move forward, backward, bidirectionally, or randomly. (If the path is a circle, the choices are counter-clockwise and clockwise instead of forward and backward.) If you specify random motion on a path, each time the point is moved it’s given a brand-new random position somewhere on the path.

An independent point always moves randomly. Each time it moves, its new position depends both on its previous position and on its location within the window. A point moving slowly takes only small steps from its previous position, whereas a point moving quickly takes larger steps. If the point is near an edge of the window or outside the window, it’s more likely to move toward the center of the window than away from it. In this way,randomly moving independent points usually remain visible.

A parameter has a domain within which it is animated and can increase in value, decrease in value, change bidirectionally, or change randomly within that domain. To set the default domain for a parameter, use the Parameter Properties panel. To set a parameter’s domain and direction for an Animation button, use the Animate Properties panel.

Motion Speed

Use the Motion Controller, the Increase/Decrease Speed commands, or an Animation button to set the speed of an animating object relative to the medium speed for that object.

You can set the ideal medium speed for points using System Preferences.The actual motion speed depends both on this setting and on your computer.

The Motion Controller displays medium speed as speed 1.0. Sketchpad attempts to keep this speed constant, but if your sketch is complex or your computer is busy with other tasks, medium speed may be slightly slower than requested in System Preferences.

Once-Only Motion

When you create an Animation button, you can specify that an object moves one time only. If the object is moving randomly, this means that one press of the button causes the object to move one time to a new random position. If the object is not moving randomly, once-only motion means that the object will stop once it returns to its starting position.