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<h1 data-toc-skip>3D Models programmatically</h1>
<small class="dont-index">Source: <a href="https://github.com/ryantimpe/brickr/blob/master/vignettes/models-from-program.Rmd"><code>vignettes/models-from-program.Rmd</code></a></small>
<div class="hidden name"><code>models-from-program.Rmd</code></div>
</div>
<div id="getting-started" class="section level2">
<h2 class="hasAnchor">
<a href="#getting-started" class="anchor"></a>Getting started</h2>
<p>The <code>bricks_from_*</code> series of functions creates 3D models of LEGO bricks from a variety of input formats.</p>
<p>Use <code><a href="../reference/bricks_from_coords.html">bricks_from_coords()</a></code> to programmatically build 3D LEGO models rather than manually drawing them in a spreadsheet or table. Prove the function with a data frame with x, y, and z coordinates, along with an official LEGO color name for each point.</p>
</div>
<div id="a-simple-programmed-model" class="section level2">
<h2 class="hasAnchor">
<a href="#a-simple-programmed-model" class="anchor"></a>A simple programmed model</h2>
<p>Below, we create a 8x8x8 cube by expanding a data frame with the array 1:8 as the x-, y-, and z-coordinates. We then assign each row of that data frame one of three colors: Bright blue, Bright yellow, or Bright red.</p>
<div class="sourceCode" id="cb1"><html><body><pre class="r"><span class="no">use_colors</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"Bright blue"</span>, <span class="st">"Bright yellow"</span>, <span class="st">"Bright red"</span>)
<span class="no">cube</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/expand.grid.html">expand.grid</a></span>(
<span class="kw">x</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fl">8</span>,
<span class="kw">y</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fl">8</span>,
<span class="kw">z</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fl">8</span>
)
<span class="no">cube</span>$<span class="no">Color</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="no">use_colors</span>, <span class="fu"><a href="https://rdrr.io/r/base/nrow.html">nrow</a></span>(<span class="no">cube</span>), <span class="kw">replace</span> <span class="kw">=</span> <span class="fl">TRUE</span>, <span class="kw">prob</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">5</span>, <span class="fl">3</span>, <span class="fl">1</span>))
<span class="no">cube</span> <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/bricks_from_coords.html">bricks_from_coords</a></span>() <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/build_bricks.html">build_bricks</a></span>()
<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="kw">userMatrix</span> <span class="kw">=</span> <span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/matrices.html">rotate3d</a></span>(<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="st">"userMatrix"</span>), <span class="fl">1.1</span>*<span class="no">pi</span>/<span class="fl">4</span>, <span class="fl">0</span>, <span class="fl">0</span> ,<span class="fl">1</span>))</pre></body></html></div>
<p><img src="models-from-program_files/figure-html/bricks_6-1.png" width="384"></p>
<p>Using the same logic, we can build a sphere with a specified radius, and then apply rules to color each brick based on its coordinates.</p>
<div class="sourceCode" id="cb2"><html><body><pre class="r"><span class="no">radius</span> <span class="kw">&lt;-</span> <span class="fl">4</span>
<span class="no">sphere_coords</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/expand.grid.html">expand.grid</a></span>(
<span class="kw">x</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>((<span class="no">radius</span>*<span class="fl">2.5</span>)),
<span class="kw">y</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>((<span class="no">radius</span>*<span class="fl">2.5</span>)),
<span class="kw">z</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>((<span class="no">radius</span>/(<span class="fl">6</span>/<span class="fl">5</span>)*<span class="fl">2.5</span>)) <span class="co">#A brick is 6/5 taller than it is wide/deep</span>
) <span class="kw">%&gt;%</span>
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate</a></span>(
<span class="co">#Distance of each coordinate from center</span>
<span class="kw">dist</span> <span class="kw">=</span> (((<span class="no">x</span>-<span class="fu"><a href="https://rdrr.io/r/base/mean.html">mean</a></span>(<span class="no">x</span>))^<span class="fl">2</span> + (<span class="no">y</span>-<span class="fu"><a href="https://rdrr.io/r/base/mean.html">mean</a></span>(<span class="no">y</span>))^<span class="fl">2</span> + (<span class="no">z</span>-<span class="fu"><a href="https://rdrr.io/r/base/mean.html">mean</a></span>(<span class="no">z</span>))^<span class="fl">2</span>)^(<span class="fl">1</span>/<span class="fl">2</span>)),
<span class="kw">Color</span> <span class="kw">=</span> <span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when</a></span>(
<span class="co">#Yellow stripes on the surface with a 2to4 thickness</span>
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/between.html">between</a></span>(<span class="no">dist</span>, (<span class="no">radius</span>-<span class="fl">1</span>), <span class="no">radius</span>) <span class="kw">&amp;</span> (<span class="no">x</span>+<span class="no">y</span>+<span class="no">z</span>) <span class="kw">%%</span> <span class="fl">6</span> <span class="kw">%in%</span> <span class="fl">0</span>:<span class="fl">1</span> ~ <span class="st">"Bright yellow"</span>,
<span class="co">#Otherwise, sphere is blue</span>
<span class="no">dist</span> <span class="kw">&lt;=</span> <span class="no">radius</span> ~ <span class="st">"Bright blue"</span>
))
<span class="no">sphere_coords</span> <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/bricks_from_coords.html">bricks_from_coords</a></span>() <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/build_bricks.html">build_bricks</a></span>(<span class="kw">rgl_lit</span> <span class="kw">=</span> <span class="fl">FALSE</span>, <span class="kw">outline_bricks</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="kw">userMatrix</span> <span class="kw">=</span> <span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/matrices.html">rotate3d</a></span>(<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="st">"userMatrix"</span>), <span class="fl">1.1</span>*<span class="no">pi</span>/<span class="fl">4</span>, <span class="fl">0</span>, <span class="fl">0</span> ,<span class="fl">1</span>))</pre></body></html></div>
<p><img src="models-from-program_files/figure-html/bricks_7-1.png" width="384"></p>
<p>The option <code>outline_bricks = TRUE</code> adds a black outline around the edges of the bricks. Setting <code>rgl_lit = FALSE</code> turns off automated lighting effects from rgl. Changing these two inputs together renders bricks in a more cartoon fashion.</p>
</div>
<div id="it-takes-a-village" class="section level2">
<h2 class="hasAnchor">
<a href="#it-takes-a-village" class="anchor"></a>It takes a village</h2>
<p>Rather than directly writing a data frame for a model, you can write a function that returns a data frame with x, y, z, and Color coordinates given initial starting parameters.</p>
<p>Below, the function <code>brick_house()</code> creates a LEGO house with randomized colors. The x- and y-coordinates and the size of the house are inputs to the functions.</p>
<div class="sourceCode" id="cb3"><html><body><pre class="r"><span class="no">brick_house</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">x_coord</span> <span class="kw">=</span> <span class="fl">0</span>, <span class="no">y_coord</span> <span class="kw">=</span> <span class="fl">0</span>, <span class="no">width</span><span class="kw">=</span><span class="fl">6</span>, <span class="no">length</span><span class="kw">=</span><span class="fl">5</span>, <span class="no">height</span><span class="kw">=</span><span class="fl">7</span>){
<span class="no">roof_colors</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"Dark orange"</span>, <span class="st">"Dark brown"</span>, <span class="st">"Medium nougat"</span>, <span class="st">"Medium stone grey"</span>)
<span class="no">roof_col</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="no">roof_colors</span>, <span class="fl">1</span>)
<span class="no">house_colors</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="st">"Bright blue"</span>, <span class="st">"Bright red"</span>, <span class="st">"Dark red"</span>, <span class="st">"Dark azur"</span>, <span class="st">"Nougat"</span>, <span class="st">"Bright reddish violet"</span>)
<span class="no">house_col</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="no">house_colors</span>, <span class="fl">1</span>)
<span class="no">house_coords</span> <span class="kw">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/expand.grid.html">expand.grid</a></span>(
<span class="kw">x</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="no">width</span>, <span class="kw">y</span> <span class="kw">=</span> <span class="fl">1</span>:<span class="no">length</span>, <span class="kw">z</span> <span class="kw">=</span> (<span class="fl">1</span>:<span class="no">height</span>)+<span class="fl">1</span>
) <span class="kw">%&gt;%</span>
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate</a></span>(
<span class="kw">roof</span> <span class="kw">=</span> (<span class="no">z</span> <span class="kw">&gt;</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>((<span class="fl">1</span>/<span class="fl">2</span>)*<span class="no">height</span>)),
<span class="kw">Color</span> <span class="kw">=</span> <span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when</a></span>(
<span class="co">#Roof</span>
<span class="no">roof</span> <span class="kw">&amp;</span> (<span class="fu"><a href="https://rdrr.io/r/base/MathFun.html">abs</a></span>(<span class="no">y</span> - <span class="fu"><a href="https://rdrr.io/r/base/Round.html">floor</a></span>(<span class="no">length</span>/<span class="fl">2</span>) -<span class="fl">1</span>) <span class="kw">&lt;=</span> (<span class="no">height</span>-<span class="no">z</span>)) ~ <span class="no">roof_col</span>,
<span class="no">roof</span> ~ <span class="fl">NA_character_</span>,
<span class="co">#Door and windows</span>
<span class="no">x</span> <span class="kw">==</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">width</span>/<span class="fl">2</span>) <span class="kw">&amp;</span> <span class="no">y</span><span class="kw">==</span><span class="fl">1</span> <span class="kw">&amp;</span> <span class="no">z</span> <span class="kw">&lt;=</span> <span class="fl">3</span> ~ <span class="fl">NA_character_</span>,
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/between.html">between</a></span>(<span class="no">x</span>, <span class="fl">2</span>, <span class="no">width</span>-<span class="fl">1</span>) <span class="kw">&amp;</span> <span class="no">x</span> <span class="kw">%%</span> <span class="fl">2</span> <span class="kw">==</span> <span class="fl">0</span> <span class="kw">&amp;</span> <span class="no">y</span> <span class="kw">&gt;</span> <span class="fl">1</span> <span class="kw">&amp;</span> <span class="no">z</span> <span class="kw">==</span> <span class="fl">3</span> ~ <span class="fl">NA_character_</span>,
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/between.html">between</a></span>(<span class="no">y</span>, <span class="fl">2</span>, <span class="no">length</span>-<span class="fl">1</span>) <span class="kw">&amp;</span> <span class="no">y</span> <span class="kw">%%</span> <span class="fl">2</span> <span class="kw">==</span> <span class="fl">0</span> <span class="kw">&amp;</span> <span class="no">z</span> <span class="kw">==</span> <span class="fl">3</span> ~ <span class="fl">NA_character_</span>,
<span class="no">x</span> <span class="kw">%in%</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">1</span>, <span class="no">width</span>) <span class="kw">|</span> <span class="no">y</span> <span class="kw">%in%</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">1</span>, <span class="no">length</span>) ~ <span class="no">house_col</span>),
<span class="kw">x</span> <span class="kw">=</span> <span class="no">x</span>+<span class="no">x_coord</span>,
<span class="kw">y</span> <span class="kw">=</span> <span class="no">y</span>+<span class="no">y_coord</span>
)
<span class="fu"><a href="https://rdrr.io/r/base/function.html">return</a></span>(<span class="no">house_coords</span>)
}
<span class="co">#Build one house</span>
<span class="fu">brick_house</span>() <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/bricks_from_coords.html">bricks_from_coords</a></span>() <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/build_bricks.html">build_bricks</a></span>()
<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="kw">userMatrix</span> <span class="kw">=</span> <span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/matrices.html">rotate3d</a></span>(<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="st">"userMatrix"</span>), <span class="fl">1.1</span>*<span class="no">pi</span>/<span class="fl">4</span>, <span class="fl">0</span>, <span class="fl">0</span> ,<span class="fl">1</span>))</pre></body></html></div>
<p><img src="models-from-program_files/figure-html/bricks_8-1.png" width="384"></p>
<p>Next, we write one more function, <code>brick_street()</code> to build a road and grass foundation. The, for an arbitrary number of houses and neighborhood size, use <code><a href="https://purrr.tidyverse.org/reference/map2.html">purrr::pmap_df</a></code> to generate many houses and place them along the road.</p>
<div class="sourceCode" id="cb4"><html><body><pre class="r"><span class="no">brick_street</span> <span class="kw">&lt;-</span> <span class="kw">function</span>(<span class="no">width</span> <span class="kw">=</span> <span class="fl">100</span>, <span class="no">length</span> <span class="kw">=</span> <span class="fl">40</span>){
<span class="fu"><a href="https://rdrr.io/r/base/expand.grid.html">expand.grid</a></span>(<span class="kw">x</span><span class="kw">=</span><span class="fl">1</span>:<span class="no">width</span>, <span class="kw">y</span><span class="kw">=</span><span class="fl">1</span>:<span class="no">length</span>, <span class="kw">z</span><span class="kw">=</span><span class="fl">1</span>) <span class="kw">%&gt;%</span>
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate</a></span>(
<span class="kw">Color</span> <span class="kw">=</span> <span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when</a></span>(
<span class="no">y</span> <span class="kw">==</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span>(<span class="no">length</span>/<span class="fl">2</span>) <span class="kw">&amp;</span> <span class="no">x</span> <span class="kw">%%</span> <span class="fl">4</span> <span class="kw">%in%</span> <span class="fl">1</span>:<span class="fl">4</span> ~ <span class="st">"Bright yellow"</span>,
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/between.html">between</a></span>(<span class="no">y</span>, <span class="no">length</span>/<span class="fl">2</span> -<span class="fl">5</span>, <span class="no">length</span>/<span class="fl">2</span> +<span class="fl">5</span>) ~ <span class="st">"Dark stone grey"</span>,
<span class="fl">TRUE</span> ~ <span class="st">"Dark green"</span>
))
}
<span class="co">#Build a village, houses on 2 sides of a street</span>
<span class="no">n_houses</span> <span class="kw">=</span> <span class="fl">14</span>
<span class="no">sz</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fl">100</span>, <span class="fl">40</span>)
<span class="fu"><a href="https://rdrr.io/r/base/list.html">list</a></span>(<span class="kw">x_coord</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/seq.html">seq</a></span>(<span class="fl">10</span>, <span class="no">sz</span>[<span class="fl">1</span>]-<span class="fl">10</span>, <span class="kw">by</span> <span class="kw">=</span> <span class="fl">12</span>), <span class="no">n_houses</span>/<span class="fl">2</span>),
<span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/seq.html">seq</a></span>(<span class="fl">10</span>, <span class="no">sz</span>[<span class="fl">1</span>]-<span class="fl">10</span>, <span class="kw">by</span> <span class="kw">=</span> <span class="fl">12</span>), <span class="no">n_houses</span>/<span class="fl">2</span>)),
<span class="kw">y_coord</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span>(<span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="no">sz</span>[<span class="fl">2</span>]/<span class="fl">2</span>-<span class="fl">15</span>, <span class="no">n_houses</span>/<span class="fl">2</span>), <span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span>(<span class="no">sz</span>[<span class="fl">2</span>]/<span class="fl">2</span>+<span class="fl">10</span>, <span class="no">n_houses</span>/<span class="fl">2</span>)),
<span class="kw">width</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="fl">4</span>:<span class="fl">10</span>, <span class="no">n_houses</span>, <span class="kw">replace</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
<span class="kw">length</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="fl">5</span>:<span class="fl">8</span>, <span class="no">n_houses</span>, <span class="kw">replace</span> <span class="kw">=</span> <span class="fl">TRUE</span>),
<span class="kw">height</span> <span class="kw">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sample.html">sample</a></span>(<span class="fl">7</span>:<span class="fl">9</span>, <span class="no">n_houses</span>, <span class="kw">replace</span> <span class="kw">=</span> <span class="fl">TRUE</span>)
) <span class="kw">%&gt;%</span>
<span class="kw pkg">purrr</span><span class="kw ns">::</span><span class="fu"><a href="https://purrr.tidyverse.org/reference/map2.html">pmap_df</a></span>(<span class="no">brick_house</span>) <span class="kw">%&gt;%</span>
<span class="kw pkg">dplyr</span><span class="kw ns">::</span><span class="fu"><a href="https://dplyr.tidyverse.org/reference/bind.html">bind_rows</a></span>(<span class="fu">brick_street</span>(<span class="no">sz</span>[<span class="fl">1</span>], <span class="no">sz</span>[<span class="fl">2</span>])) <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/bricks_from_coords.html">bricks_from_coords</a></span>() <span class="kw">%&gt;%</span>
<span class="fu"><a href="../reference/build_bricks.html">build_bricks</a></span>()
<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="kw">userMatrix</span> <span class="kw">=</span> <span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/matrices.html">rotate3d</a></span>(<span class="kw pkg">rgl</span><span class="kw ns">::</span><span class="fu"><a href="https://rdrr.io/pkg/rgl/man/par3d.html">par3d</a></span>(<span class="st">"userMatrix"</span>), <span class="fl">1.1</span>*<span class="no">pi</span>/<span class="fl">4</span>, <span class="no">pi</span>/<span class="fl">4</span>, <span class="fl">0</span> ,<span class="fl">1</span>))</pre></body></html></div>
<p><img src="models-from-program_files/figure-html/bricks_9-1.png" width="384"></p>
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