Matrices (The Chickadee Game Toolkit)

From 25c5eac5e6ca1035db1eddd7bea9ac78531da57e Mon Sep 17 00:00:00 2001 From: David Thompson Date: Thu, 28 Dec 2023 11:23:49 -0500 Subject: Delete manuals! Good riddance! These are hosted on files.dthompson.us now! --- manuals/chickadee/Matrices.html | 409 ---------------------------------------- 1 file changed, 409 deletions(-) delete mode 100644 manuals/chickadee/Matrices.html (limited to 'manuals/chickadee/Matrices.html') diff --git a/manuals/chickadee/Matrices.html b/manuals/chickadee/Matrices.html deleted file mode 100644 index bf65917..0000000 --- a/manuals/chickadee/Matrices.html +++ /dev/null @@ -1,409 +0,0 @@ - - - - - - -Matrices (The Chickadee Game Toolkit) - - - - - - - - - - - - - - - - - - - - -

5.2.4 Matrices

- -

The (chickadee math matrix) module provides an interface for -working with the most common type of matrices in game development: 4x4 -transformation matrices. -

Another Note About Performance -

Much like the vector API, the matrix API is commonly used in -performance critical code paths. In order to reduce the amount of -garbage generated and improve matrix multiplication performance, there -are many procedures that perform in-place modifications of matrix -objects. -

5.2.4.1 3x3 Matrices

- -

Procedure: make-matrix3 aa ab ac ba bb bc ca cb cc: Return a new 3x3 initialized with the given 9 values in column-major -format. -

- -

Procedure: make-null-matrix3: Return a new 3x3 matrix with all values initialized to 0. -

- -

Procedure: make-identity-matrix3

Return a new 3x3 identity matrix. Any matrix multiplied by the -identity matrix yields the original matrix. This procedure is -equivalent to the following code: -

(make-matrix3 1 0 0
-              0 1 0
-              0 0 1)
-

- -

Procedure: matrix3? obj: Return #t if obj is a 3x3 matrix. -

- -

Procedure: matrix3= m1 m2: Return #t if m1 is the same matrix as m2. -

- -

Procedure: matrix3-copy matrix: Return a new 3x3 matrix that is a copy of matrix. -

- -

Procedure: matrix3* . matrices

Return a new 3x3 matrix containing the product of multiplying all of -the given matrices. -

Note: Remember that matrix multiplication is not commutative! -

- -

Procedure: matrix3-translate v: Return a new 3x3 matrix that represents a translation by v, a 2D -vector. -

- -

Procedure: matrix3-scale s: Return a new 3x3 matrix that represents a scaling along the x and y -axes by the scaling factor s, a number or 2D vector. -

- -

Procedure: matrix3-rotate angle: Return a new 3x3 matrix that represents a rotation by angle -radians. -

- -

Procedure: matrix3-transform matrix v: Return a new 2D vector that is v as transformed by the 3x3 -matrix matrix. -

- -

Procedure: matrix3-inverse matrix: Return the inverse of matrix. -

- -

The following procedures perform in-place, destructive updates to 3x3 -matrix objects: -

Procedure: matrix3-copy! src dest: Copy the contents of matrix src to dest. -

- -

Procedure: matrix3-identity! matrix: Modify matrix in-place to contain the identity matrix. -

- -

Procedure: matrix3-mult! dest a b: Multiply the 3x3 matrix a by the 3x3 matrix b and store -the result in the 3x3 matrix dest. -

- -

Procedure: matrix3-translate! matrix v: Modify matrix in-place to contain a translation by v, a 2D -vector. -

- -

Procedure: matrix3-scale! matrix s: Modify matrix in-place to contain a scaling along the x and y -axes by the scaling factor s, a number or 2D vector. -

- -

Procedure: matrix3-rotate! matrix angle: Modify matrix in-place to contain a rotation by angle -radians. -

- -

Procedure: matrix3-transform! matrix v: Modify the 2D vector v in-place to contain v as -transformed by the 3x3 matrix matrix. -

- -

Procedure: matrix3-inverse! matrix target: Compute the inverse of matrix and store the results in -target. -

- -

5.2.4.2 4x4 Matrices

- -

Procedure: make-matrix4 aa ab ac ad ba bb bc bd ca cb cc cd da db dc dd: -
Return a new 4x4 matrix initialized with the given 16 values in -column-major format. -

- -

Procedure: make-null-matrix4: Return a new 4x4 matrix with all values initialized to 0. -

- -

Procedure: make-identity-matrix4

Return a new 4x4 identity matrix. Any matrix multiplied by the -identity matrix yields the original matrix. This procedure is -equivalent to the following code: -

(make-matrix4 1 0 0 0
-              0 1 0 0
-              0 0 1 0
-              0 0 0 1)
-

- -

Procedure: matrix4? obj: Return #t if obj is a 4x4 matrix. -

- -

Procedure: matrix4= m1 m2: Return #t if m1 is the same matrix as m2. -

- -

Procedure: matrix4-copy matrix: Return a new 4x4 matrix that is a copy of matrix. -

- -

Procedure: matrix4* . matrices

Return a new 4x4 matrix containing the product of multiplying all of -the given matrices. -

Note: Remember that matrix multiplication is not commutative! -

- -

Procedure: matrix4-inverse matrix

Return the inverse of matrix. -

A matrix multiplied by its inverse is the identity matrix, thought not -always exactly due to the nature of floating point numbers. -

- -

Procedure: orthographic-projection left right top bottom near far: -
Return a new 4x4 matrix that represents an orthographic (2D) -projection for the horizontal clipping plane top and -bottom, the vertical clipping plane top and bottom, -and the depth clipping plane near and far. -

- -

Procedure: perspective-projection fov aspect-ratio near far: -
Return a new 4x4 matrix that represents a perspective (3D) projection -with a field of vision of fov radians, an aspect ratio of -aspect-ratio, and a depth clipping plane defined by near -and far. -

- -

Procedure: matrix4-translate x: Return a new 4x4 matrix that represents a translation by x, a 2D -vector, a 3D vector, or a rectangle (in which case the bottom-left -corner of the rectangle is used). -

- -

Procedure: matrix4-scale s: Return a new 4x4 matrix that represents a scaling along the X, Y, and -Z axes by the scaling factor s, a real number. -

- -

Procedure: matrix4-rotate q: Return a new 4x4 matrix that represents a rotation about an arbitrary -axis defined by the quaternion q. -

- -

Procedure: matrix4-rotate-z theta: Return a new 4x4 matrix that represents a rotation about the Z axis by -theta radians. -

- -

The following procedures perform in-place, destructive updates to 4x4 -matrix objects: -

Procedure: matrix4-copy! src dest: Copy the contents of matrix src to dest. -

- -

Procedure: matrix4-identity! matrix: Modify matrix in-place to contain the identity matrix. -

- -

Procedure: matrix4-mult! dest a b: Multiply the 4x4 matrix a by the 4x4 matrix b and store -the result in the 4x4 matrix dest. -

- -

Procedure: matrix4-inverse! matrix target: Compute the inverse of matrix and store the result in -target. -

- -

Procedure: matrix4-translate! matrix x: Modify matrix in-place to contain a translation by x, a 2D -vector, a 3D vector, or a rectangle (in which case the bottom-left -corner of the rectangle is used). -

- -

Procedure: matrix4-scale! matrix s: Modify matrix in-place to contain a scaling along the X, Y, and -Z axes by the scaling factor s, a real number. -

- -

Procedure: matrix4-rotate! matrix q: Modify matrix in-place to contain a rotation about an arbitrary -axis defined by the quaternion q. -

- -

Procedure: matrix4-rotate-z! matrix theta: Modify matrix in-place to contain a rotation about the Z axis by -theta radians. -

- -

Procedure: matrix4-2d-transform! matrix [#:origin] [#:position] [#:rotation] [#:scale] [#:shear]: -
Modify matrix in-place to contain the transformation described -by position, a 2D vector or rectangle, rotation, a scalar -representing a rotation about the Z axis, scale, a 2D vector, -and shear, a 2D vector. The transformation happens with respect -to origin, a 2D vector. If an argument is not provided, that -particular transformation will not be included in the result. -

- -

Procedure: matrix4-transform! matrix v: Modify the 2D vector v in-place by multiplying it by the 4x4 -matrix matrix. -

- -

- - - - - - -- cgit v1.2.3