From 32adfa759cd4b289a7093b7c7971638295eb30aa Mon Sep 17 00:00:00 2001 From: ickk Date: Thu, 14 Sep 2023 12:01:56 +1000 Subject: [PATCH] add license & update readme --- LICENSE-APACHE | 176 +++++++++++++++++++++++++++++++++++++++++++++++++ LICENSE-MIT | 19 ++++++ README.md | 57 ++++++++++------ ega/Cargo.toml | 1 + 4 files changed, 233 insertions(+), 20 deletions(-) create mode 100644 LICENSE-APACHE create mode 100644 LICENSE-MIT diff --git a/LICENSE-APACHE b/LICENSE-APACHE new file mode 100644 index 0000000..d9a10c0 --- /dev/null +++ b/LICENSE-APACHE @@ -0,0 +1,176 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md index f8f841a..ab8a195 100644 --- a/README.md +++ b/README.md @@ -1,28 +1,45 @@ -# EGA +EGA +=== -This project is a work-in-progress implementation of a PGA library for 3D -computer graphics. +Toy implementation of a PGA library for computer graphics. --- -This library is an implementation of an R{3,0,1} geometric algebra, which is -the smallest geometric algebra that can encode 3D euclidian geometry. +"Projective Geometric Algebra" is a relatively small GA suitible for encodeing +3D euclidian geometry & transformation. -Other algebras in the same family include the R{2,0,1} 2D PGA, and the R{4,1} -Conformal Geometric Algebra. The CGA can also encode euclidian geometry (among -other things like spheres), however its full multivector has 25 elements. This -means a full geometric product is quite expensive to compute in CGA. +The algebra is 4 dimensional, and a full-multivector contains 16 values, so it +is comparable to the common 4x4 matrix from linear algebra. -Compared to CGA (R{4,1}), the R{3,0,1} PGA (this library), has a multivector -with only 16 elements and a computational cost roughly equivalent to a 4x4 -matrix in linear algebra. +The implementation here is meant to be straight forward and sparse. Not +everything is implemented, and while there are many many tests it's possible +there are some bugs. -Furthermore, this library uses the type system along with the product rules of -the algebra to reduce the computational & memory costs where possible. For -instance we store only the vector components `e0`,`e1`,`e2`,`e3` as a `Vector` -and we know that the outer-product of a vector with another vector is a -bivector (on a 6 element basis). so `Vector.meet(Vector) -> Bivector`. This -helps to avoid full-16 element products in many cases. +The products largely follow the Cayley tables from [bivector.net]. -See [bivector.net](https://bivector.net/PGA4CS.html) for more information -about the mathematics. +[bivector.net]: (https://bivector.net) + +In the future I may try an implementation of the algebra +[rigidgeometricalgebra.org], which uses slightly different notation & products. + +[rigidgeometricalgebra.org]: (https://rigidgeometricalgebra.org) + +--- + +Some references: + +- L. Dorst and S. D. Keninck, “A Guided Tour to the Plane-Based Geometric Algebra PGA,” bivector.net, https://bivector.net/PGA4CS.pdf, 2022. +- C. G. Gunn, “Course notes Geometric Algebra for Computer Graphics SIGGRAPH 2019,” bivector.net, https://bivector.net/PROJECTIVE_GEOMETRIC_ALGEBRA.pdf, 2019. +- L. Dorst, S. Mann, and D. Fontijne, Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. Morgan Kaufmann Publishers, 2007. +- A. Macdonald, Linear and Geometric Algebra. Charleston, SC: Alan Macdonald, 2017. +- E. Lengyel, Foundations of Game Engine Development. Lincoln, CA: Terathon Software LLC, 2016. + + +License +------- + +This crate is dual-licensed under either the +[Apache license, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0) +or the +[MIT license](http://opensource.org/licenses/MIT) +at your option. diff --git a/ega/Cargo.toml b/ega/Cargo.toml index 887e57b..7c9fbbc 100644 --- a/ega/Cargo.toml +++ b/ega/Cargo.toml @@ -2,6 +2,7 @@ name = "ega" version = "0.0.0" edition = "2021" +license = "MIT OR Apache-2.0" [dependencies] libm = { version = "0.2.0", optional = true }