Collection of static utilities
Static methods
staticlargestEig2x2(m1:Float, m12:Float, m2:Float):Vec3
"Compute largest eigenvalue and associated eigenvector of a symmetric 2x2 matrix. Solves characteristic equation. Inputs: three elements of matrix (upper-left, diag, lower-right) Outputs: largest (in magnitude) eigenvector/value" -- Trimesh2
staticldltdc(A:Array<Array<Float>>, rdiag:Array<Float>):Bool
"LDL^T decomposition of a symmetric positive definite matrix (and some other symmetric matrices, but fragile since we don't do pivoting). Like Cholesky, but no square roots, which is important for small N. Reads diagonal and upper triangle of matrix A. On output, lower triangle of A holds LD, while rdiag holds D^-1. Algorithm from Golub and van Loan." -- Trimesh2
staticldltsl(A:Array<Array<Float>>, rdiag:Array<Float>, b:Array<Float>, x:Array<Float>):Void
"Solve Ax=b after ldltdc. x is allowed to be the same as b." -- Trimesh
staticinlinematIden():Array<Float>
Returns a 4x4 identiy matrix (row-major, flat)
Returns:
the identity matrix
staticinlinematMult(A:Array<Float>, B:Array<Float>):Array<Float>
Multiply two 4x4 matrices (row-major, flat)
Parameters:
A | first matrix |
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B | second matrix |
Returns:
the matrix product
staticinlinematProj(f:Float, v:Vec3):Vec3
Project a 3D point onto 2D plane with pinhole camera model situated at (0,0,0) pointing toward +z
Parameters:
f | focal length |
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v | the vector |
Returns:
a 2D point (with zeroed z component)
staticinlinematRotx(a:Float):Array<Float>
Returns a 4x4 matrix for rotating around x axis (row-major, flat)
Parameters:
a | the angle in radians |
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Returns:
the rotation matrix
staticinlinematRoty(a:Float):Array<Float>
Returns a 4x4 matrix for rotating around y axis (row-major, flat)
Parameters:
a | the angle in radians |
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Returns:
the rotation matrix
staticinlinematRotz(a:Float):Array<Float>
Returns a 4x4 matrix for rotating around z axis (row-major, flat)
Parameters:
a | the angle in radians |
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Returns:
the rotation matrix
staticinlinematScal(x:Float, y:Float, z:Float):Array<Float>
Returns a 4x4 scaling matrix (row-major, flattend)
Parameters:
x | scale along x axis |
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y | scale along x axis |
z | scale along x axis |
Returns:
the scaling matrix
staticinlinematTrfm(A:Array<Float>, v:Vec3):Vec3
Transform a 3D vector using a 4x4 matrix (row-major, flat)
Parameters:
A | the transformation matrix |
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v | the vector |
Returns:
new vector after transformation
staticinlinematTrsl(x:Float, y:Float, z:Float):Array<Float>
Returns a 4x4 translation matrix (row-major, flat)
Parameters:
x | translation along x axis |
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y | translation along x axis |
z | translation along x axis |
Returns:
the translation matrix
staticinlinemin(a:Int, b:Int):Int
MIN() for integers
Parameters:
a | first integer |
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b | second integer |
Returns:
the lesser of the inputs
staticinlinenextMod3(i:Int):Int
i + 1 modulo 3. "This way of computing it tends to be faster than using %" -- Trimesh2
staticinlineprevMod3(i:Int):Int
i - 1 modulo 3. "This way of computing it tends to be faster than using %" -- Trimesh2
staticinlinerndInt(x:Float):Int
Round float to integer
Parameters:
x | the float to be rounded |
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Returns:
closest integer
staticinlineuniformHemisphereSampler():Vec3
Uniform random sampler on unit hemisphere (+z)
Returns:
a random point that lies on the hemisphere
staticwriteFile(filename:String, content:String):Void
Save a string to a file on disk
Parameters:
filename | path to the file |
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content | content to be written |