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If we draw both circles, two new points are created at their intersections. Drawing lines between the two original points and one of these new points completes the construction of an equilateral triangle. Therefore, in any geometric problem we have an initial set of symbols (points and lines), an algorithm, and some results.
Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Geometric Supposer, which does not have draggable objects, but allows students to study pre-defined shapes. Nearly all of the following programs are DGEs.
A pencil of planes, is the set of planes through a given straight line in three-space, called the axis of the pencil. The pencil is sometimes referred to as a axial-pencil [7] or fan of planes or a sheaf of planes. [8] For example, the meridians of the globe are defined by the pencil of planes on the axis of Earth's rotation.
3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display.
The pencil holder, thumb screws, brass pivot and branches are all well built. They are used for scribing circles and stepping off repetitive measurements [5] with some accuracy. A reduction compass or proportional dividers is used to reduce or enlarge patterns while conserving angles. Ellipse drawing compasses are used to draw ellipse.
In this method, the user creates a 2D shape which traces the outline of an object from a photograph or a drawing. [3] The user then uses a second image of the subject from a different angle and extrudes the 2D shape into 3D, again following the shape’s outline. This method is especially common for creating faces and heads.
Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis ...
Loft is a method to create complicated smooth 3D shapes in CAD and other 3D modeling software. Planar cross-sections of the desired shape are defined at chosen locations. Algorithms find a smooth 3D shape that fit these cross-sections. Designers can modify the shape through choice of fitting algorithm and input parameters.
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