Artists drawing technical illustrations often require that precise relationships hold among picture elements. For example, certain line segments should be horizontal, parallel, or congruent. Interactive illustration systems in the past have provided techniques such as grids and constraints to facilitate precise positioning. Both of these techniques have significant limitations. Grids provide only a small fraction of the desired types of precision. Constraints, while very powerful, require the user to specify and add extra structure that is often difficult to understand and time consuming to manipulate. We introduce an interactive technique, intelligent dragging, as a compromise between the convenience of grids and the power of constraints.

Intelligent dragging is based on the familiar idea of snapping the display cursor to points and curves using a gravity function. The new idea is that a set of gravity active points, lines and circles called alignment objects are automatically constructed from hints given by the user plus heuristics about typical editing behavior. The result is a system with as much power as a ruler, compass, protractor, and T-square drafting set, but little time is spent moving the tools and setting up the constructions. The name "intelligent dragging" is meant to suggest that the program is making intelligent guesses about which gravity active objects to compute, but the user is performing all scene modifications individually by dragging scene objects until they snap onto gravity active objects.

Intelligent dragging can be seen as an extension to the idea of gravity active grids (used in illustrators such as Griffin, Gremlin, MacDraw®, and Star® Graphics [Stone80] [Opperman84] [MacDraw84] [Lipkie82]) or as a diluted form of constraint-based system (such as Sketchpad, ThingLab, and Juno [Sutherland84] [Borning79] [Nelson85]. As in a grid system, the cursor may snap to gravity active objects provided by the system. However, the set of gravity active objects is richer and varies with the current scene and with the operation being performed. As in a constraint-based system, points can be placed to satisfy angle constraints, slope constraints, and distance constraints. However, with intelligent dragging, constraints are solved two at a time, with the user explicitly controlling the placement of each point, and the constraints are forgotten as soon as they are used rather than becoming part of the data structure.

Intelligent dragging is currently implemented as part of the Gargoyle two dimensional illustrator, running in the Cedar programming environment [Swinehart80], on the Xerox Dorado high-performance personal workstation [Pier83]. All the figures in this paper except figure 7 were created with Gargoyle.

In Section 2 we will present intelligent dragging in more detail. Section 3 is an analysis of design issues for geometric precision techniques, comparing grids, constraints and intelligent dragging. Section 4 presents more detail on the implementation of intelligent dragging. Section 5 summarizes our results.

This section describes how intelligent dragging is used to construct shapes and perform transformations. In Gargoyle, a special point called the the caret can be placed with precision using gravity. The caret is distinct from the cursor in that the cursor always moves with the mouse, while the caret can stray from the cursor if a gravity active object attracts it. In construction operations a new point is always placed at the position of the caret. Positioning operations use the position of the caret as a parameter. When adding or moving a point to an object, affected line segments are adjusted in realtime using the technique called rubber-banding [Newman79]. Transformed objects are smoothly dragged into position. The user specifies via a menu or by typing any special points of interest and what kinds of precision are currently of interest. How many alignment objects to generate and where to place them is determined automatically. Alignment objects are visible only when the user is in the process of moving a point or object and are drawn in gray so they may be easily distinguished.

Figure 1 shows how a user would adjust a point in an existing triangle to make the base horizontal.

Figure 2 demonstrates construction of an equilateral triangle 0.75 inch on a side with its base at 30 degrees to horizontal. Constructing the triangle takes six steps:

The whole process takes six keystrokes and all but two of these would be needed to draw any triangle. Note that it is impossible to construct an equilateral triangle using only a square grid and in most constraint systems, only a triangle with a horizontal base would be easy.

Interactive transformations based on the current position of the cursor are already present in commercial illustrators. However, the ability to take advantage of alignment objects makes it easy to perform these operations with precision. Each transformation is performed in three steps. First, the objects to be transformed are selected. Second, the caret is placed at an initial position in the scene. Gravity and alignment objects can be used to choose this position with precision. Third, the selected objects are smoothly transformed (translated, rotated, or scaled) using the displacement between the original position of the caret and the new (constantly updated) position of the caret to determine the current transformation. Like the original caret position, the new caret position can be snapped to alignment objects. We will discuss the operations translate, rotate, and scale in more detail here.

When performing translation, we simply add a displacement vector (old caret - new caret) to the original position of each selected object to get its new position. We move one polygon to touch another by selecting a point on the selected polygon in the first step, and a point on the target polygon at the end. Figure 3 shows how point-parameterized translation can be used to align two rectangles; the caret is snapped onto a 90 degree slope line in this example.

The center of rotation, called the anchor, is placed by positioning the caret and invoking the Drop Anchor command. During rotation, the angle of rotation is kept equal to the angle through which the caret displacement vector has moved from its initial position. Consider the example in figure 4. We place the anchor point at the base of an arrow, make the initial selection at its tip (Point A), and make the final selection on the object we would like the arrow to point to (Point B).

The anchor point is also used as the center of scaling. The magnitude of scaling is the ratio of the new caret displacement vector to the original caret displacement vector. This transformation can be used to scale one object until one of its dimensions matches a dimension of another object. In figure 5 the square is enlarged to fit onto an edge of the hexagon.

The ideal tool is powerful but easy to use. Good tool design, therefore, requires a compromise between functionality and complexity of user interface. We measure the functionality of a geometric precision tool by examining which of a set of geometric relationships can be expressed directly. This set of relationships must be weighed against the total number of commands the user must learn and the time taken to specify all the arguments and invoke each command.

Ease of use involves more than reduction of commands and keystrokes. A system that is easy to use will be predictable, require user input in proportion to the difficulty of the task, and be free from catastrophic failures which destroy hours of work. We will show that intelligent dragging makes it easy to reach these goals.

In this section we will describe the sets of relationships we use to define the power of a geometric tool, and describe some important factors in making a system easy to use. In the process, we will compare intelligent dragging to grids and constraints.

In this section we will provide more detail about three important aspects of intelligent dragging: How we select and position alignment objects, how a set of lines of known slope and circles of known radius can be used to provide all of the constraints mentioned in Section 3 and how we get intelligent dragging to work in real time.

There are three construction techniques used in computer illustration systems. Grid systems have been commercial successes because they are easy to learn and implement. Constraint-based systems are constantly discussed in the literature because of their great power. We have shown that ruler and compass type construction systems are a viable compromise. Most of the advantages that we claim for intelligent dragging are advantages of the ruler and compass approach. In particular, it handles a wide range of alignment types, works at any rotation, and provides constraints which are easy to add, delete, and modify. For example, Qubix Graphics Systems has begun to demonstrate a technical illustration workstation which employs the ruler, compass and protractor paradigm.

The obvious drawback of a construction approach is that setting up the construction may take quite a bit of time. Intelligent dragging tries to reduce construction time by taking advantage of the repetition which is present in many constructions; often the same slope or distance is needed repeatedly; often a polygon's vertex is aligned with other vertices of that same polygon. We believe the result is almost as easy to learn to use as grids, while providing most of the power of constraint systems.

While ruler and compass construction is not inherently computationally expensive, intelligent dragging is; many alignment objects must be drawn and many intersection points must be computed. However, the computational requirements are bounded, because the user will turn off alignment objects when the screen becomes too cluttered. Improvements in graphics hardware will make the technique feasible in low-cost workstations in the near future.

Work is in progress to extend intelligent dragging to the editing of free-form curves and to three dimensional objects.

We can introduce curves in a straightforward manner if the curves are controlled by points. In addition, we would like to extend our system to make alignments based on the local tangent to a curve to provide a simple way to position objects on curves.

One of the motivations for this work is to develop better ways to edit objects quickly in three dimensions. In three dimensions, the grid approach is impractical because drawing a full three dimensional grid puts so many lines on the screen that the user has trouble identifying the proper grid point, and notifying the system of the point chosen. Constraint-based approaches are also difficult to use. Some progress has been made by Lin et al. towards using constraints in three dimensions to alter dimensions in mechanical assemblies [Lin81]. It is more difficult to use constraints to provide a quick-sketch capability because, in three dimensions, there is an explosion of degrees of freedom which need to be constrained requiring the production of a large number of constraints. A modified version of intelligent dragging might be successful in providing a precise three dimensional quick-sketch capability.