Sly: Transforms

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4.2.3 Transforms

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(use-modules (sly math transform))
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Transforms are 4x4 transformation matrices. Matrices are the -fundamental structure for modeling affine transformations such as -translation, rotation, and scaling. Complex transformations are -created by composing many simpler ones with the transform* -procedure. -

It’s a good idea to use transforms in a functional manner by treating -them as immutable. This is made easy because almost every procedure -in this module returns a new transform rather than mutating an -existing one. However, in some cases it is necessary to use mutable -transforms via transform*! for performance reasons. -

Scheme Procedure: make-transform aa ab ac ad ba bb bc bd ca cb cc cd da db dc dd: Create a new transform initialized with the given 16 values in -column-major format. -

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Scheme Variable: null-transform: A transform composed entirely of zeroes. -

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Scheme Variable: identity-transform: The multiplicative identity transform. -

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Scheme Syntax: transform? obj: Return #t if obj is a transform. -

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Scheme Syntax: transform-matrix transform: Return the underlying 4x4 floating point array for transform. -

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Scheme Procedure: transpose transform: Return a transform that is the transpose of transform. -

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Scheme Procedure: transform-vector2 transform v: Apply transform to the 2D vector v. -

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Scheme Procedure: transform-position transform: Return a 3D vector containing the positional data stored in -transform. -

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Scheme Procedure: transform+ . transforms: Return the sum of transforms. Return null-transform if -called without any arguments. -

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Scheme Procedure: transform* . transforms: Return the product of transforms. Return identity-transform if -called without any arguments. -

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Scheme Procedure: transform*! dest a b: Multiply a and b, storing the result in dest. -

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Scheme Procedure: translate v: Create a new transform that translates by the 2D or 3D vector v. -

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Scheme Procedure: scale v
Scheme Procedure: scale scalar: Create a new transform that scales by the 2D or 3D vector v, or -by scalar to scale evenly in all dimensions. -

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Scheme Procedure: rotate-x angle: Create a new transform that rotates the x axis by angle radians. -

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Scheme Procedure: rotate-y angle: Create a new transform that rotates the y axis by angle radians. -

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Scheme Procedure: rotate-z angle: Create a new transform that rotates the z axis by angle radians. -

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Scheme Procedure: rotate q: Convert the quaternion q into a rotation transform. -See Quaternions for more information. -

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One of the most common composite transformations is a translation -multiplied by a scale multiplied by a rotation. The -build-transform procedure is a convenience procedure for this -case. -

Scheme Procedure: build-transform [#:position=(vector3 0 0 0)] [#:scale=1] [#:rotation=null-quaternion]

Build a transform by multiplying the following transforms: -

translation by position -
rotation by rotation -
scaling by scale -

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The procedures below are useful for creating projection and view -matrices for cameras. See Cameras for more details. -

Scheme Procedure: orthographic-projection left right top bottom near far: Create a new transform that represents an orthographic projection for -the vertical clipping plane left and right, the horizontal -clipping plane top and bottom, and the depth clipping -plane near and far. -

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Scheme Procedure: perspective-projection field-of-vision aspect-ratio near far: Create a new transform that represents a perspective projection with a -field-of-vision in degrees, the desired aspect-ratio, and -the depth clipping plane near and far. -

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Scheme Procedure: look-at eye center [up=(vector3 0 1 0)]: Create a view transform that looks from 3D vector eye at the 3D -vector center, with the 3D vector up indicating which -direction points up. -

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