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APM - The abbreviation for Artists' Perspective Modeler.
Attitude Parameters - The combination of the viewing distance to the airplane, and its angular rotation in azimuth, elevation, roll, and offsets that produces a particular viewing aspect. Also, see Fixed Parameters, Parameters, and Variable Parameters.
Azimuth - An angular measurement used to orient the airplane to the desired viewing aspect by rotating it about the vertical (Y) axis of the picture plane. Also, see Elevation, Roll, and Rotation.
Auxiliary View - When the airplane's plan view is positioned obliquely to the edges of the Horizontal plane, its side and front views are projected onto the profile and/or frontal planes as Auxiliary views.
Cartoon - A full-size preliminary sketch of a picture to be copied or traced onto an art medium.
Center of Vision (CV) - The point on the picture plane where the eyelevel line, the central vertical line, and the central visual ray intersect. Also, see Picture Plane.
Central Visual Ray (CVR) - The central line of sight in the cone of vision. It extends from the eye position to the center of vision on the picture plane. No matter the direction of sight, CVR has a constant perpendicular relationship with the picture plane. The true length viewing distance of a perspective is between EP and CV along the CVR.
Cone of Vision (CoV) - The cone-shaped field of vision, normally about 50†, that extends from the eye to the world beyond. The central visual ray is the centerline of the cone. If the cone extends beyond 30† in a perspective drawing, the extremities of the image tend to become distorted. Whether looking up, down or sidewise, CVR is always parallel to the line of sight.
Coordinate Axes - (Cartesian coordinates.) A set of numbers that locates the position of a point from a plane. In APM the numbers for length are represented by x, width by y, and height by z.
CV Cross Hair -
Elevation - An angular measurement used to orient the airplane to the desired viewing aspect by rotating it about the horizontal (X) axis of the picture plane. See also: Azimuth, Roll, and Rotation.
Eye Position (EP) - The location of the observer's eye relative to the picture plane. It's at the same distance above the ground as the horizon. Also, see Picture Plane Environment.
Fixed Parameters- The set of parameters - Distance, Azimuth, Elevation, Roll, x-offset, y-offset, z-offset, and Size - that fix the viewing aspect (attitude) of the airplane in a specific exercise. Also, see Attitude Parameters, Parameter, and Variable Parameters.
Horizon Line - A trace of the horizon plane on the picture plane. It also serves as the vanishing line. Also, see Picture Plane Environment, and Trace.
Horizontal Plane - See Picture Plane Environment.
Initial Position - In the initial position--before rotations and offsets--the airplane is head-on to the viewer with its origin point 0 coincident with the picture plane CV. (See Line of Sight diagram.) In the initial position the x- [dimensions] increase away from the viewer (behind the picture plane), +y- to the right, -y- to the left, and z- upward. The effect of any rotation, or any combination of rotations is to pivot the airplane about the CV to the desired viewing aspect. Also, see Origin Point. See also: Offsets
Line of Sight - An imaginary straight line joining the observer's eye with the airplane viewed.
Mathematical Logic - APM is a mathematical system and therefore requires that certain rules be followed. Among them: The absolute values of numbers increase from zero, regardless of their sign, (+) or (-); Negative numbers must be preceded by a minus (-) sign.
Mathematical Model - The set of x y z variable dimensions that define the length, width, height, size, shape and contours of an airplane, and from which a three-dimensional model or prototype can be built.
Measuring Planes - The triad of numbers (represented by x, y, and z) locate a point in space by its distance from three fixed planes that intersect one another at right angles. The "0" point of the x- y- and z-axes is at the intersection of the planes. The x-y plane is horizontal; the x-z plane is in profile; and the y-z plane is frontal.
Monocular Vision - Literally, seeing with one eye. With monocular vision the perception of size or distance can only be inferred by comparison with other airplanes of known size or at known distances. Cameras and telescopes, for example, are monocular devices. Photographs and "perspective" drawings are monocular perceptions. If viewed from other than the camera's, or the artist's eye position, pictures themselves are seen in perspective.)
Offsets - Initially, the airplane 0 (zero point) is coincident with the picture plane CV. Offsets are auxiliary x y z (length, width, height) dimensions that are added to (or subtracted from, as the case may be) the airplane's entire set of primary x y z dimensions. The effect of offsets is to move the airplane longitudinally (x), laterally (y) and vertically (z) from its initial position, to a better compositional location within the picture frame, or to position multiple airplanes at different flight attitudes and distances within a composition. (All airplanes offset within the composition will be at their correct "perspective" relative to CV and to one another.) Xoff, yoff or zoff can be used singly or in any combination, and with any combination of rotations. See also: Offsets and Rotation
One-Point Perspective - A perspective projection in which one set of horizontal lines is parallel to the viewer's line of sight. The lines are foreshortened and they converge to a single vanishing point at the Center of Vision (CV) on the horizon. The other set of horizontals, and the verticals are parallel to the picture plane; they do not converge, and they can be measured.
Origin Point "0" - All x y z dimensions taken from the 3-view drawing are measured from their origin at the 0 point. The APM program initially places the head-on view of the airplane on the Picture Plane (PP) with 0 positioned at the Center of Vision (CV.)
It's also the point of origin of the offsets, which are added to (or subtracted from, as the case may be) the entire set of variables to displace, or relocate, the airplane from CV on the picture plane. Also, see Offsets, Three-View and Variables.
Orthographic - If an observer's eye position is at an infinite distance from an airplane, the rays from points on the airplane to the observer's eye will become parallel. The image projected onto the picture plane will be formed by perpendiculars from the airplane and will have its same dimensions. Thus, a three-view drawing is an orthographic projection. Also, see Perspective.
Parameter - A quantity whose value varies with the circumstances of its application. Also, see Attitude Parameters, Fixed Parameters, and Variable Parameters.
Perspective - If an observer's eye position is at a nearby distance from an airplane, the image projected on a picture plane where it is pierced by rays from the airplane will be practically the same as that formed in the observer's eye. Also, see Orthographic, Picture Plane and Picture Plane Environment.
Perspective Projection - A three-dimensional airplane in pictorial form as it is seen on a two-dimensional picture plane where it is pierced by rays from points on the airplane to the observer's eye. The vehicle for the transformation is geometry, itself a branch of mathematics.
Picture plane (PP) - Technically, a transparent two-dimensional surface, perpendicular to the line of sight, on which an image is projected where it is pierced by rays from an airplane to the eye. In a more literal sense, it can be a sheet of paper, a canvas, a wall, a billboard or any flat surface suitable for the artist's purpose. The picture plane is ALWAYS perpendicular to the line of sight (the Central Visual Ray.)
Picture Plane Axes -
Picture Plane Environment -
Positive/Negative - APM mathematics requires that data with negative values be preceded by a minus (-) sign.
Roll - An angular measurement used to orient the airplane to the desired viewing aspect by rotating it about the line of sight (Z) axis of the picture plane. See also: Azimuth, Elevation and Rotation.
Recalculate - See Calculate.
Rotation - In mathematical perspective systems (e.g., APM) the airplane is rotated in degrees of Azimuth, Elevation and Roll about three mutually perpendicular axes on the Picture Plane to bring it to the desired viewing aspect. Rotation can be from 0† to 360† in either a positive or negative direction as indicated by the arrows in the diagram. Azimuth rotation is about the vertical (Y) axis. Elevation rotation is about the horizontal (X) axis. Roll rotation is about the line of sight (Z) axis. Negative values must be preceded by a minus (-) sign. Rotation can be about a single axis, or a composite of any two, or all three axes. The effects can be A, E, R, A+E, A+R, E+R, or A+E+R.
Scale - The ratio between the dimensions of a representation and those of the airplane; e.g., a scale of one 1:48 is 1 inch = 48 inches, or (1/4-inch = 1 foot.)
Three-Dimensional Airplane - A material thing that occupies space. To name a few; trains, planes and automobiles, cereal boxes, cream pitchers, eagles, houses, horses, pyramids and airplanes are three-dimensional objects. They have in common: width, length and height.
Three-Dimensional Projection - If the airplane is placed within a matrix of three mutually perpendicular transparent planes, Horizontal, Profile and Frontal, its image may be projected onto the planes to provide its three defining views: The Plan, Side and Front views. Conversely, the three views may be projected inward to form the three dimensional airplane. Also, see Auxiliary View, Three-View Drawing.
Three-Point Perspective - In three-point perspective, horizontal lines converge to points V1 and V2 on the Horizon line, above the eyelevel line (EL), and to the left and right of the CV. Vertical lines converge to V3 on a line perpendicular to the horizon line. The perpendicular line passes through the CV.
3-View Drawing - A basic three-view drawing describes the shape of an airplane and specifies its size in every detail. The views are usually: a plan (top) view, a side view and a front view placed adjacent to one another on mutually perpendicular planes. Data provided by the views are: Length (x), Width (y) and Height (z). Each adjacent view shares a dimension with its neighbor. Each view has a corresponding opposite view. Also, see Auxiliary View, Orthographic and Three-Dimensional Projection. (See also, Variable Parameters, Zero Point.)
Trace - An imaginary line that remains on a surface where another surface or line has passed through it. The horizon line and the central vertical line on the picture plane are traces of the horizontal plane and the central vertical plane.
Two-point perspective - In two-point perspective, the sets of horizontal lines point in different directions and converge to vanishing points (V1 and V2) on the horizon to the left and right of the CV. If the projection is rotated 90† in either direction about the Line of Sight, the vanishing points will be above and below the CV, and the effect will be that of looking up, or down at the airplane. Also, see, One-Point Perspective, Three-Point Perspective.
Vanishing Line - A horizon line where parallel line sets converge in a point
Vanishing Point (VP) - A point on a horizon line to which any two or more lines that are in fact parallel, if extended indefinitely, will converge. Any system of parallel lines that is not parallel to the picture plane will appear to converge at a vanishing point. Also, see One-, Two-, and Three-Point Perspective.
Variable Parameters - The triad of x y z (length, width, height) dimensions that specify the location of a point in space relative to the 0 point of a three-dimensional airplane. (The table below shows the x y z values for the eight corners of a 3 x 3 x 3 cube.) Also, see Coordinates, Three-view drawing and Zero Point.
Vertical Plane - See Picture Plane Environment illustration.
Viewing Distance (D) - The true-length distance along the central visual ray from the eye position to the center of vision on the picture plane.
Work Sheet -
x y z and X Y Z -
Yaw, Pitch, Roll -