Transform literals

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3.1.3.3 Transform literals

Most transform literals are formed by constructors. These are summarized in the following table.

Constructor Param types Description
rotate(A,P,X) scalar,point,vector Rotate A degrees about point P with axis X according to the right hand rule. See Right hand rule. P and X are both optional and default to the origin and the z-axis respectively.
translate(X) vector Translate by X.
scale(S) scalar Scale uniformly by factor S.
scale(V) vector Scale along each axis by components of V.
project() — Same as scale([1,1,0]).
project(S) scalar Perspective projection with view center at origin and projection plane z=-S.
perspective(S) scalar Perspective transform identical to project(S) except that the z-coordinate of the transformed result is pseudodepth, usable by the hidden surface algorithm.
view(E,D,U) point,vector,vector View transform similar to that of OpenGL's. The eye point E is translated to the origin while a rotation is also applied that makes the view direction vector D and the view “up” vector U point in the negative z- and the y-directions respectively. If U is omitted, it defaults to [0,1,0]. When U is omitted, D may be also; it defaults to (0,0,0)-(E), a vector pointing from the eye toward the origin.
view(E,L,U) point,point,vector An alternate form of view(E,D,U) above where the view direction parameter D is replaced with a “look at” point L, i.e., a point where the viewer is focusing her attention. This form of view is equivalent to view(E, (L)-(E), U), where (L)-(E) is a direction vector. U is optional and defaults to [0,1,0].
[[a_11,a_12,a_13,a_14]
[a_21,a_22,a_23,a_24]
[a_31,a_32,a_33,a_34]
[a_41,a_42,a_43,a_44]]
16 scalars Direct transform matrix definition. Each of the a_ij is a scalar expression. See text for details.
The project constructor is not generally useful because it defeats hidden surface removal by collapsing the scene onto a single plane. It is a special purpose transform for drawing pictures of scenes where three-dimensional objects are being projected onto planes. See, for example, Overview.

Constructor	Param types	Description
`rotate(A,P,X)`	scalar,point,vector	Rotate `A` degrees about point `P` with axis `X` according to the right hand rule. See Right hand rule. `P` and `X` are both optional and default to the origin and the z-axis respectively.
`translate(X)`	vector	Translate by `X`.
`scale(S)`	scalar	Scale uniformly by factor `S`.
`scale(V)`	vector	Scale along each axis by components of `V`.
`project()`	—	Same as `scale([1,1,0])`.
`project(S)`	scalar	Perspective projection with view center at origin and projection plane z=-`S`.
`perspective(S)`	scalar	Perspective transform identical to `project(S)` except that the z-coordinate of the transformed result is pseudodepth, usable by the hidden surface algorithm.
`view(E,D,U)`	point,vector,vector	View transform similar to that of `OpenGL`'s. The eye point `E` is translated to the origin while a rotation is also applied that makes the view direction vector `D` and the view “up” vector `U` point in the negative z- and the y-directions respectively. If `U` is omitted, it defaults to [0,1,0]. When `U` is omitted, `D` may be also; it defaults to `(0,0,0)-(E)`, a vector pointing from the eye toward the origin.
`view(E,L,U)`	point,point,vector	An alternate form of `view(E,D,U)` above where the view direction parameter `D` is replaced with a “look at” point `L`, i.e., a point where the viewer is focusing her attention. This form of view is equivalent to `view(E, (L)-(E), U)`, where `(L)-(E)` is a direction vector. `U` is optional and defaults to [0,1,0].
`[[a_11,a_12,a_13,a_14]` `[a_21,a_22,a_23,a_24]` `[a_31,a_32,a_33,a_34]` `[a_41,a_42,a_43,a_44]]`	16 scalars	Direct transform matrix definition. Each of the a_ij is a scalar expression. See text for details.

The direct transform constructor allows direct entry of a 4x4 transformation matrix. Most 3d graphics systems, including sketch, use 4-dimensional homogeneous coordinates internally. These are transformed by multiplication with 4x4 matrices. The built-in constructors (rotate, scale, etc.) are all translated internally to such 4x4 matrices. For more information on homogeneous coordinate transformations, see any good computer graphics textbook. The direct transform feature of sketch allows you to enter a matrix of your own choice. There are not many cases where this is useful, but if you do need it, you need it badly!