Geometric Primitive: Exploring Foundations and Applications in Computer Vision

By Fouad Sabry

What is Geometric Primitive

In the fields of vector computer graphics, computer-aided design (CAD) systems, and geographic information systems, the term "geometric primitive" refers to the most basic geometric shape that the system is able to process. However, the subroutines that are responsible for drawing the relevant objects are also referred to as "geometric primitives" in some instances. The point and straight line segment primitives are considered to be the most "primitive" primitives because they were the only ones that early vector graphics systems had.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Geometric primitive

Chapter 2: Dimension

Chapter 3: Vector graphics

Chapter 4: Computational geometry

Chapter 5: Composite Bézier curve

Chapter 6: Bézier surface

Chapter 7: Non-uniform rational B-spline

Chapter 8: Global illumination

Chapter 9: Constructive solid geometry

Chapter 10: Solid modeling

(II) Answering the public top questions about geometric primitive.

(III) Real world examples for the usage of geometric primitive in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Geometric Primitive.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 5, 2024

Book preview

Chapter 1: Geometric primitive

In vector computer graphics, CAD systems, and geographic information systems, a geometric primitive (or prim) is the system's simplest (i.e., atomic or irreducible) geometric shape (draw, store). Occasionally, the subroutines that draw the related objects are also referred to as geometric primitives. Early vector graphics systems only supported the most basic primitives, the point and the straight line segment.

In constructive solid geometry, primitives are basic geometric figures such as the cube, cylinder, sphere, cone, pyramid, and torus.

Modern 2D computer graphics systems can operate with curve primitives (segments of straight lines, circles, and more complex curves) in addition to shape primitives (boxes, arbitrary polygons, circles).

Common two-dimensional primitives consist of lines, points, and polygons, Although some individuals prefer to view triangles as elementary,, due to the fact that every polygon may be built from triangles.

All other graphic elements are constructed from these basic elements.

Three dimensionally, Positioned triangles or polygons in three-dimensional space can be used as primitives to describe more complicated three-dimensional shapes.

In certain instances, curves (such as Bézier curves, circles, etc.) could be regarded as primitives; other instances, curves are complicated shapes made from numerous straight lines, primitive shapes.

The collection of geometric primitives is determined by the region's dimensions:

A point is a single position with no height, breadth, or depth (0-dimensional).

One-dimensional line or curve, having length but no width, however a linear feature may curve in a higher-dimensional space.

Surface, whether planar or curved and two-dimensional, has length and width.

Three-dimensional volumetric area or solid with length, width, and depth.

The terrain surface is commonly referred to be 2 1/2-dimensional in GIS because just the upper surface has to be represented. Consequently, elevation can be conceived as a scalar field attribute or function of two-dimensional space, which affords it a number of data modeling advantages over genuine three-dimensional objects. A shape with any of these dimensions greater than zero is composed of an unlimited number of points. As digital systems are limited, only a subset of a shape's points may be saved. Thus, vector data structures often describe geometric primitives using a strategic sample, structured in structures that allow the software to interpolate the remainder of the shape at the time of analysis or display using the methods of computational geometry.

A Point is a single Cartesian coordinate in a coordinate system. Some data models provide Multipoint attributes consisting of many unconnected points.

A polygonal chain or polyline is a list of points in sequence (termed vertices in this context).

The software is supposed to interpolate, as a parametric curve, the geometry of the line between neighboring points in the list, typically a straight line, Nevertheless, various sorts of curves are commonly accessible, consisting of circular arcs, cubic splines, and Bézier curves.

Some of these curves necessitate the definition of additional points that are not on the line itself, however are employed for parametric control.

The boundary of a two-dimensional region is represented by a polygon, which is a closed polyline. This boundary is anticipated to be utilized by the software to divide 2-dimensional space into an interior and exterior. Some data models permit a single feature to consist of numerous polylines, which may link to form a single closed boundary, may represent a series of disconnected regions (such as Hawaii), or may represent a region with holes (e.g., a lake with an island).

A parametric shape is a conventional two-dimensional or three-dimensional shape that is defined by a minimal number of parameters, such as an ellipse specified by two points at its foci, or three points at its center, vertex, and co-vertex.

A Polyhedron or Polygon mesh is a collection of connected polygon faces in three-dimensional space that entirely enclose a volumetric region. In other applications, such as terrain modeling, closure may not be required or may be implied. This surface will be used by the software to divide three-dimensional space into an interior and outside. A triangular mesh is a subclass of polyhedron in which all faces must be triangles. It is the only polygon that will always be planar, including the Triangulated irregular network (TIN) often used in geographic information systems.

A parametric mesh portrays a three-dimensional surface using a network of parametric functions, similar to a spline or Bézier curve in two dimensions.

Non-uniform rational B-spline is the most used structure (NURBS), supported by the majority of CAD and animation programs.

In the history of Geographic information systems, numerous vector data structures and formats have been developed, but they all share the fundamental characteristic of storing a core set of geometric primitives to describe the location and range of geographic events. Point locations are nearly typically measured using a common Earth-based coordinate system, such as the spherical Geographic coordinate system (latitude/longitude) or the planar Universal Transverse Mercator. They must also contain a collection of properties for each geographic feature in addition to its shape. Historically, this has been accomplished using the data structures, data formats, and even software of relational databases.

Early vector formats, such as POLYVRT, the ARC/INFO Coverage, and the Esri shapefile, provide a fundamental set of geometric primitives: points, polylines, and polygons, but only in two-dimensional space and with only straight line interpolation for the latter two. Also added were TIN data structures for expressing terrain surfaces as triangle meshes. Since the mid-1990s, new formats have been developed to broaden the range of possible primitives, which are typically defined by the Simple Features specification of the Open Geospatial Consortium. Common extensions to geometric primitives include three-dimensional coordinates for points, lines, and polygons, a fourth dimension to represent a measured attribute or time, curved segments in lines and polygons, text annotation as a type of geometry, and polygon meshes for three-dimensional objects.

Often, a depiction