-
Notifications
You must be signed in to change notification settings - Fork 3
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
* Branch commit log: .gitignore: add OUTLINE.md misc/subdirs.mk: use $O or out/ as builddir if unset .github/workflows/pages.yml: name workflow doc/copyright.ini: fix missing licenses doc/mkdocs.yml: fix site URL, cleanup, improve nav doc/*: remove old sections doc/index.md: merge intro and install info doc/mkdocs.yml: add comment about future feature doc/Makefile.mk: use new tab for external links doc/Makefile.mk: add comments doc/mkdocs.yml: trim Doxygen generation of mkdoxy * doc/Makefile.mk: remove useless listing of anonymous namespaces doc/mkdocs.yml: enableMathJAX rendering * doc/ch-appendix.md: simplify for MathJAX * doc/javascripts/mathjax.js: detect MathJAX blocks * doc/Makefile.mk: allow extra Javascript doc/mkdocs.yml: use new nav structure doc/how-audio.md: add "Howto Setup Audio (Linux)" * doc/Makefile.mk: add doc/how-audio.md to doc files * doc/mkdocs.yml: add doc/how-audio.md to nav doc/tut-play.md: add "Tutorial 1: Starting to Play Notes" * doc/Makefile.mk: add doc/tut-play.md to doc files * doc/mkdocs.yml: add doc/tut-play.md to nav doc/mkdocs.yml: enable markdown_extensions doc/index.md: add mkdocs front page * doc/Makefile.mk: add index.md to docs * doc/mkdocs.yml: add index.md to nav .github/workflows/pages.yml: build docu with mkdocs and deploy pages doc/Makefile.mk: extend mkdocs, add pdf doc/Makefile.mk: add mkdocs rule doc/mkdocs.yml: build modernized docs with mkdocs, mkdoxy misc/Dockerfile.jammy: update build dependencies, add mkdocs ui/eslintrc.js: allow attrs w/o newlines package.json: update Vue, Electron, Lit and development dependencies package.json: add moxygen Signed-off-by: Tim Janik <[email protected]>
- Loading branch information
Showing
17 changed files
with
599 additions
and
218 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,61 @@ | ||
| # This Source Code Form is licensed MPL-2.0: http://mozilla.org/MPL/2.0 | ||
| # | ||
| # Workflow for mkdocs building and deploying to GitHub Pages | ||
| # | ||
| # Linting: xclip -sel c <.github/workflows/pages.yml # https://rhysd.github.io/actionlint/ | ||
| # | ||
| name: Deploy mkdocs site to Pages | ||
|
|
||
| on: | ||
| # Runs on pushes targeting the default branch | ||
| push: | ||
| branches: ["trunk"] | ||
|
|
||
| # Allows you to run this workflow manually from the Actions tab | ||
| workflow_dispatch: | ||
|
|
||
| # Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages | ||
| permissions: | ||
| contents: read | ||
| pages: write | ||
| id-token: write | ||
|
|
||
| # Allow only one concurrent deployment, skipping runs queued between the run in-progress and latest queued. | ||
| # However, do NOT cancel in-progress runs as we want to allow these production deployments to complete. | ||
| concurrency: | ||
| group: "pages" | ||
| cancel-in-progress: false | ||
|
|
||
| jobs: | ||
| # Build job | ||
| build: | ||
| runs-on: ubuntu-latest | ||
| container: { image: 'ghcr.io/tim-janik/anklang-ci:jammy-latest' } | ||
| steps: | ||
| - name: Checkout Anklang | ||
| run: | | ||
| pwd && ls -al | ||
| rm -rf * .[^.]* ..?* | ||
| git clone --recurse-submodules https://github.com/tim-janik/anklang.git . | ||
| - name: Setup Pages | ||
| id: pages | ||
| uses: actions/configure-pages@v5 | ||
| - run: echo -e 'prefix=/\n CC=clang \n CXX=clang++ \n CLANG_TIDY=clang-tidy ' > config-defaults.mk | ||
| - run: make mkdocs -j`nproc` | ||
| - run: ls -al out/site/ | ||
| - name: Upload artifact | ||
| uses: actions/upload-pages-artifact@v3 | ||
| with: | ||
| path: ./out/site/ | ||
|
|
||
| # Deployment job | ||
| deploy: | ||
| environment: | ||
| name: github-pages | ||
| url: ${{ steps.deployment.outputs.page_url }} | ||
| runs-on: ubuntu-latest | ||
| needs: build | ||
| steps: | ||
| - name: Deploy to GitHub Pages | ||
| id: deployment | ||
| uses: actions/deploy-pages@v4 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
|
|
@@ -4,6 +4,7 @@ | |
| /.submodule-stamp | ||
| /.vscode/ | ||
| /BACKLOG.md | ||
| /OUTLINE.md | ||
| /TAGS | ||
| /bun.lockb | ||
| /compile_commands.json | ||
|
|
||
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,124 +1,115 @@ | ||
| \appendix | ||
|
|
||
| # Appendix | ||
|
|
||
| | ||
|
|
||
| ## One-dimensional Cubic Interpolation | ||
|
|
||
| \def\V#1{V_{#1}} | ||
|
|
||
| \def\W#1{W_{#1}} | ||
|
|
||
| \def\w#1{w_{#1}} | ||
|
|
||
| With four sample values $\V0$, $\V1$, $\V2$ and $\V3$, cubic interpolation approximates | ||
| the curve segment connecting $\V1$ and $\V2$, by using the beginning and ending | ||
| With four sample values $V_0$, $V_1$, $V_2$ and $V_3$, cubic interpolation approximates | ||
| the curve segment connecting $V_1$ and $V_2$, by using the beginning and ending | ||
| slope, the curvature and the rate of curvature change to construct a cubic | ||
| polynomial. | ||
|
|
||
|
|
||
| The cubic polynomial starts out as: | ||
|
|
||
| (@a) $f(x) = \w3 x^3 + \w2 x^2 + \w1 x + \w0$ | ||
| * a) $f(x) = w_3 x^3 + w_2 x^2 + w_1 x + w_0$ | ||
|
|
||
| Where $0 <= x <= 1$, specifying the sample value of the curve segment between | ||
| $\V1$ and $\V2$ to obtain. | ||
| $V_1$ and $V_2$ to obtain. | ||
|
|
||
| To calculate the coefficients $\w0,…,\w3$, we set out the following conditions: | ||
| To calculate the coefficients $w_0…w_3$, we set out the following conditions: | ||
|
|
||
| (@b) $f(0) = \V1$ | ||
| (@c) $f(1) = \V2$ | ||
| (@d) $f'(0) = \V1'$ | ||
| (@e) $f'(1) = \V2'$ | ||
| * b) $f(0) = V_1$ | ||
| * c) $f(1) = V_2$ | ||
| * d) $f'(0) = V_1'$ | ||
| * e) $f'(1) = V_2'$ | ||
|
|
||
| We obtain $\V1'$ and $\V2'$ from the respecting slope triangles: | ||
| We obtain $V_1'$ and $V_2'$ from the respecting slope triangles: | ||
|
|
||
| (@f) $\V1' = \frac {\V2 - \V0} {2}$ | ||
| (@g) $\V2' = \frac {\V3 - \V1} {2}$ | ||
| * f) $V_1' = \frac {V_2 - V_0} {2}$ | ||
| * g) $V_2' = \frac {V_3 - V_1} {2}$ | ||
|
|
||
| With (@f) → (@d) and (@g) → (@e) we get: | ||
| With (f)→(d) and (g)→(e) we get: | ||
|
|
||
| (@h) $f'(0) = \frac {\V2 - \V0} {2}$ | ||
| (@i) $f'(1) = \frac {\V3 - \V1} {2}$ | ||
| * h) $f'(0) = \frac {V_2 - V_0} {2}$ | ||
| * i) $f'(1) = \frac {V_3 - V_1} {2}$ | ||
|
|
||
| The derivation of $f(x)$ is: | ||
|
|
||
| (@j) $f'(x) = 3 \w3 x^2 + 2 \w2 x + \w1$ | ||
| * j) $f'(x) = 3 w_3 x^2 + 2 w_2 x + w_1$ | ||
|
|
||
| From $x=0$ →(a), i.e. (b), we obtain $w_0$ and from $x=0$ →(j), | ||
| i.e. (h), we obtain $w_1$. With $w_0$ and $w_1$ we can solve the | ||
| linear equation system formed by (c)→(a) and (e)→(j) | ||
| to obtain $w_2$ and $w_3$. | ||
|
|
||
| From $x=0$ → (@a), i.e. (@b), we obtain $\w0$ and from $x=0$ → (@j), | ||
| i.e. (@h), we obtain $\w1$. With $\w0$ and $\w1$ we can solve the | ||
| linear equation system formed by (@c) → (@a) and (@e) → (@j) | ||
| to obtain $\w2$ and $\w3$. | ||
| $(c)→(a): w_3 + w_2 + \frac {V_2 - V_0} {2} + V_1 = V_2$ | ||
|
|
||
| (@c_a_) (@c) → (@a): $\w3 + \w2 + \frac {\V2 - \V0} {2} + \V1 = \V2$ | ||
| (@e_j_) (@e) → (@j): $3 \w3 + 2 \w2 + \frac {\V2 - \V0} {2} = \frac {\V3 - \V1} {2}$ | ||
| $(e)→(j): 3 w_3 + 2 w_2 + \frac {V_2 - V_0} {2} = \frac {V_3 - V_1} {2}$ | ||
|
|
||
| With the resulting coefficients: | ||
|
|
||
| $$ | ||
| \begin{aligned} | ||
| \w0 &= \V1 & &(initial\:value) \\ | ||
| \w1 &= \frac{\V2 - \V0} {2} & &(initial\:slope) \\ | ||
| \w2 &= \frac{-\V3 + 4 \V2 - 5 \V1 + 2 \V0} {2} & &(initial\:curvature) \\ | ||
| \w3 &= \frac{\V3 - 3 \V2 + 3 \V1 - \V0} {2} & &(rate\:change\:of\:curvature) | ||
| w_0 &= V_1 & &(initial\:value) \\ | ||
| w_1 &= \frac{V_2 - V_0} {2} & &(initial\:slope) \\ | ||
| w_2 &= \frac{-V_3 + 4 V_2 - 5 V_1 + 2 V_0} {2} & &(initial\:curvature) \\ | ||
| w_3 &= \frac{V_3 - 3 V_2 + 3 V_1 - V_0} {2} & &(rate\:change\:of\:curvature) | ||
| \end{aligned} | ||
| $$ | ||
|
|
||
| Reformulating (@a) to involve just multiplications and additions (eliminating power), we get: | ||
| Reformulating (a) to involve just multiplications and additions (eliminating power), we get: | ||
|
|
||
| (@k) $f(x) = ((\w3 x + \w2) x + \w1) x + \w0$ | ||
| * k) $f(x) = ((w_3 x + w_2) x + w_1) x + w_0$ | ||
|
|
||
| Based on $\V0,…,\V3$, $\w0,…,\w3$ and (@k), we can now approximate all values of the | ||
| curve segment between $\V1$ and $\V2$. | ||
| Based on $V_0…V_3$, $w_0…w_3$ and (k), we can now approximate all values of the | ||
| curve segment between $V_1$ and $V_2$. | ||
|
|
||
| However, for practical resampling applications where only a specific | ||
| precision is required, the number of points we need out of the curve | ||
| segment can be reduced to a finite amount. | ||
| Lets assume we require $n$ equally spread values of the curve segment, | ||
| then we can precalculate $n$ sets of $\W{0,…,3}[i]$, $i=[0,…,n]$, coefficients | ||
| then we can precalculate $n$ sets of $W_{0…3}[i]$, $i=[0…n]$, coefficients | ||
| to speed up the resampling calculation, trading memory for | ||
| computational performance. With $\w{0,…,3}$ in (@a): | ||
| computational performance. With $w_{0…3}$ in (a): | ||
|
|
||
| $$ | ||
| \begin{alignedat} {2} | ||
| f(x) \ &= & \frac{\V3 - 3 \V2 + 3 \V1 - \V0} 2 x^3 \ + & \\ | ||
| & & \frac{-\V3 + 4 \V2 - 5 \V1 + 2 \V0} 2 x^2 \ + & \\ | ||
| & & \frac{\V2 - \V0} 2 x \ + & \\ | ||
| & & V1 \ \ & | ||
| f(x) \ &= & \frac{V_3 - 3 V_2 + 3 V_1 - V_0} 2 x^3 \ + & \\ | ||
| & & \frac{-V_3 + 4 V_2 - 5 V_1 + 2 V_0} 2 x^2 \ + & \\ | ||
| & & \frac{V_2 - V_0} 2 x \ + & \\ | ||
| & & V1 \ \ \ \ & | ||
| \end{alignedat} | ||
| $$ | ||
|
|
||
| sorted for $\V0,…,\V4$, we have: | ||
| sorted for $V_0…V_4$, we have: | ||
|
|
||
| (@l) $$\begin{aligned} | ||
| f(x) \ = \ & \V3 \ (0.5 x^3 - 0.5 x^2) \ + & \\ | ||
| & \V2 \ (-1.5 x^3 + 2 x^2 + 0.5 x) \ + & \\ | ||
| & \V1 \ (1.5 x^3 - 2.5 x^2 + 1) \ + & \\ | ||
| & \V0 \ (-0.5 x^3 + x^2 - 0.5 x) & | ||
| \end{aligned}$$ | ||
| * l) $\begin{aligned} | ||
| f(x) \ = \ & V_3 \ (0.5 x^3 - 0.5 x^2) \ + & \\ | ||
| & V_2 \ (-1.5 x^3 + 2 x^2 + 0.5 x) \ + & \\ | ||
| & V_1 \ (1.5 x^3 - 2.5 x^2 + 1) \ + & \\ | ||
| & V_0 \ (-0.5 x^3 + x^2 - 0.5 x) & | ||
| \end{aligned}$ | ||
|
|
||
| With (@l) we can solve $f(x)$ for all $x = \frac i n$, where $i = [0, 1, 2, …, n]$ by | ||
| With (l) we can solve $f(x)$ for all $x = \frac i n$, where $i = [0, 1, 2, …, n]$ by | ||
| substituting $g(i) = f(\frac i n)$ with | ||
|
|
||
| (@m) $g(i) = \V3 \W3[i] + \V2 \W2[i] + \V1 \W1[i] + \V0 \W0[i]$ | ||
| * m) $g(i) = V_3 W_3[i] + V_2 W_2[i] + V_1 W_1[i] + V_0 W_0[i]$ | ||
|
|
||
| and using $n$ precalculated coefficients $\W{0,…,3}$ according to: | ||
| and using $n$ precalculated coefficients $W_{0…3}$ according to: | ||
|
|
||
| $$ | ||
| \begin{alignedat}{4} | ||
| m &= \frac i n \\ | ||
| \W3[i] &=& 0.5 m^3 & - & 0.5 m^2 & & \\ | ||
| \W2[i] &=& -1.5 m^3 & + & 2 m^2 & + 0.5 m & \\ | ||
| \W1[i] &=& 1.5 m^3 & - & 2.5 m^2 & & + 1 \\ | ||
| \W0[i] &=& -0.5 m^3 & + & m^2 & - 0.5 m & | ||
| W_3[i] &=& 0.5 m^3 & - & 0.5 m^2 & & \\ | ||
| W_2[i] &=& -1.5 m^3 & + & 2 m^2 & + 0.5 m & \\ | ||
| W_1[i] &=& 1.5 m^3 & - & 2.5 m^2 & & + 1 \\ | ||
| W_0[i] &=& -0.5 m^3 & + & m^2 & - 0.5 m & | ||
| \end{alignedat} | ||
| $$ | ||
|
|
||
| We now need to setup $\W{0,…,3}[0,…,n]$ only once, and are then able to | ||
| We now need to setup $W_{0…3}[0…n]$ only once, and are then able to | ||
| obtain up to $n$ approximation values of the curve segment between | ||
| $\V1$ and $\V2$ with four multiplications and three additions using (@m), | ||
| given $\V0,…,\V3$. | ||
| $V_1$ and $V_2$ with four multiplications and three additions using (m), | ||
| given $V_0…V_3$. | ||
|
|
||
|
|
||
| ## Modifier Keys | ||
|
|
@@ -141,7 +132,6 @@ none → copy (else move (else link)) | |
|
|
||
| Regarding selections, the following email provides a short summary: | ||
|
|
||
| > ~~~ | ||
| > From: Tim Janik <[email protected]> | ||
| > To: Hacking Gnomes <[email protected]> | ||
| > Subject: modifiers for the second selection | ||
|
|
@@ -201,4 +191,3 @@ Regarding selections, the following email provides a short summary: | |
| > | ||
| > --- | ||
| > ciaoTJ | ||
| > ~~~ | ||
This file was deleted.
Oops, something went wrong.
Oops, something went wrong.