2frizac

= = = =

=Solid shapes and 2d representations of 3d shapes= Example:
 * An __isometric drawing__ is best described when the horizontal line of an object is represented by lines that form 30° angles.
 * An __orthographic projection__ is a view of one side of a 3 dimensional shape

Related Links: [|Use of Isometric drawings in video games.]

=Polyhedrons, Dihedral Angles, and Spatial Relationships=

Identifying the relationships among points, lines, planes, segments, and angles in a 3d object.

 * __Polyhedron__: A polyhedron is a closed 3-dimensional shape with polygonal sides called faces.The vertices of the faces are the vertices of the polyhedron. The intersection of two faces is called an edge. Example:




 * __Parallel Planes:__ If two or more planes always remain a constant distance from each other no matter how far they are extended, then they are parallel.


 * __Line Perpendicular to a Plane:__ A line is only perpendicular to a plane if it is perpendicular to every line in the plane that it intersects.


 * __Line Parallel to a Plane:__ A line is parallel to a plane only if it is parallel to every line in the plane.

Related Links: [|Polygons in video games]
 * __Dihedral Angle:__ When two planes have a common edge, the angle that is formed from the two planes is the dihedral angle. This can be measured by measuring the angle of two rays on each face that create an angle. Example:[[image:dihedralrock.jpg width="196" height="258" caption="Dihedral angles formed by two rock planes" link="http://flickr.com/photos/adamdale/232894993/"]]

=Prisms=

__Prism:__ A prism is a polyhedron made by two congruent polygons on parallel planes with quadrilateral faces connecting the edges of the polygon __Right prism__: In a right prism, joining edges and faces are perpendicular to the bases. __Oblique prism:__ In an oblique prism, joining edges and faces are not perpendicular to the bases.

The polygons on the parallel planes are called __bases__ the remaining quadrilateral faces are called __lateral faces__.

The edges between the lateral faces that aren't also an edge of the base are called __lateral edges__.



=3 Dimensional Coordinates=

===Points in 3 dimensional space can be depicted using a 3 axes graph. The first axis (the x axis), is pointing directly front and back. The second axis (the y axis) is pointing left and right. The third axis (the z axis) is pointing up and down.===



Two pairs of axes also determines a coordinate plane. There are 3 coordinate planes. The XY plane. This plane goes left, right, front, and back but not top or bottom. The z coordinate for each point on this plane is 0. The XZ plane. This plane goes top, bottom, front, and back but not left or right. The y coordinate for each point on this plane is 0. The YZ plane. This plane goes left, right, top, and bottom but not front or back. The x coordinate for each point on this plane is 0.

When the coordinate for a point is given for a 3d graph, the order of points is alphabetic. The point (3,5,8) means that it's 3 to the front on the x axis, 5 to the right on the y axis, and 8 to the top on the z axis. The positive coordinates are front, right, and top. The negative coordinates are back, left, and bottom. For example, the point (-6,-3,-4) means that it's 6 to the back on the x axis, 3 to the left on the y axis, and 4 to the bottom on the z axis.

=Perspective Drawing=

Identify and apply basic concepts of perspective drawings.
__Vanishing point:__ The point at which two parallel lines appear to meet is the vanishing point. This is typically on the horizon of the depicted scene or image. Example:

__Sets of parallel lines:__ All lines that are parallel to each other meet at a single point. This is also a vanishing point. Example:

__Lines parallel to the ground:__ A line that is on the ground plane in a drawing and is not parallel to the picture plane will meet the horizon of the drawing is parallel to the ground.

Related Links: [|The development of the theory of perspective drawings in the Renaissance.] (First 6 paragraphs of website)