Glossary of Key Terms
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Chapter 1: Understanding 3D Space
- 3D Space
Three-dimensional space is the world we live in, having length, width, and height.
- Coordinate System
A framework to define positions in space using coordinates.
- Axis
A reference line in a coordinate system.
- Axes
Plural of Axis. The reference lines used in a coordinate system.
- Cartesian coordinate system
A coordinate system in which the position of a point in space is determined by the signed distances to three mutually perpendicular planes whose intersection defines the origin and whose axes are defined by the intersection lines of the planes.
- Vector
A quantity with both magnitude (size or length) and direction.
- Origin
The reference point (0,0,0) where the X, Y, and Z axes intersect in a coordinate system.
- Coordinates
A set of numerical values (e.g., x, y, z) that specify the exact position of a point in space relative to the origin and axes.
- X-Axis
The horizontal axis in a standard 3D Cartesian system, typically representing width or side-to-side movement.
- Horizontal
Parallel to the plane of the horizon; level. In 3D graphics, often refers to the plane defined by the X and Z axes.
- Y-Axis
The vertical axis in a standard 3D Cartesian system, typically representing height.
- Vertical
Perpendicular to the horizontal plane; upright. Associated with the Y-axis.
- Z-Axis
The axis representing depth in a standard 3D Cartesian system, perpendicular to the X-Y plane.
- Depth
The distance from front to back or away from the viewer; often associated with the Z-axis.
- Right-Handed Coordinate System
A standard orientation for 3D axes where if the fingers of the right hand curl from the positive X-axis toward the positive Y-axis, the thumb points along the positive Z-axis. Common in physics and 3D graphics.
- Magnitude
The size, length, or strength of a vector, often denoted by ||V||. It represents 'how much' of the quantity the vector describes.
- Scalar
A quantity that has only magnitude (size) but no direction (e.g., temperature, mass, speed).
- Direction
The orientation or course of a vector in space, indicating 'which way' it points.
- Components
The projections of a vector onto the coordinate axes (e.g., Vx, Vy, Vz in 3D). They represent the vector's extent along each axis.
- Unit Vectors
A vector with a magnitude (length) of exactly 1. Used primarily to indicate direction.
- Standard Basis Vectors
Unit vectors pointing along the positive directions of the coordinate axes. In 3D Cartesian coordinates, these are î (X-axis), ĵ (Y-axis), and k̂ (Z-axis).
- Reference Frame
A coordinate system used as a basis for describing the position, orientation, and motion of objects. Essentially, the perspective from which observations are made.
Chapter 2: Kinematics
- Displacement
Change in position of an object.
- Velocity
Rate of change of position with time.
- Acceleration
Rate of change of velocity with time.