BST430 Lab 7 Notes

class: ur-title, center, middle, title-slide

# BST430 Lab 7 Notes
### Andrew McDavid
### U of Rochester
### 2021-10-27 (updated: 2021-11-01)

---

### Generate an index

```r
library(tidyverse)
n = 100
scale = 3
points_df = tibble(t = ppoints(n)*scale)
points_df
```

```
## # A tibble: 100 x 1
##        t
##    <dbl>
##  1 0.015
##  2 0.045
##  3 0.075
##  4 0.105
##  5 0.135
...
```

ppoints gives `n` equally spaced points on [0, 1]

---

### Determine an outline

```r
points_df = mutate(points_df, x = rnorm(n), 
                   y_mu = (1+t)^2,
                   y = rnorm(n, mean = y_mu))
points_df
```

```
## # A tibble: 100 x 4
##        t      x  y_mu     y
##    <dbl>  <dbl> <dbl> <dbl>
##  1 0.015 -1.21   1.03 1.44 
##  2 0.045  0.277  1.09 0.617
##  3 0.075  1.08   1.16 1.22 
##  4 0.105 -2.35   1.22 0.719
...
```

---

```r
curve((1+x)^2, from = 0, to = 1)
```

Can use `curve` to help visualize components of your functions.  Other nice functions might include sin / cos to induce radial symmetry.

---

### Other attributes we can vary

```r
points_df = mutate(points_df,
  length = .5 + t/scale,
   angle = t/(scale) * pi - pi/3,
                   xend = cos(angle)*length + x,
                   yend = sin(angle)*length + y,
  # check I still know basic trig...
                   length_check = sqrt((xend-x)^2 + (yend - y)^2)
)
```

---

```r
ggplot(points_df, aes(x = x, y = y, color = t^2, xend = xend, yend = yend)) + 
  geom_segment() + 
  theme_void() + 
  scale_color_gradientn( colors = c('darkgreen', 'yellow', 'orange', 'red', 'black')) +
  guides(color = 'none') + 
  theme(plot.background = element_rect(fill = 'grey70'))
```

Maybe it looks like leaves blowing in the wind?

---

# color gradients

An important aestetic will be color gradients.  Use `scale_color_gradientn` to specify your own gradient, or check out palettes at https://www.colourlovers.com/. If you see one you like, use

```r
colourlovers::clpalette(<INTEGER ID>)
```

---

For example, for [this palette](https://www.colourlovers.com/palette/4839578/november), I can get it with

```r
pal = colourlovers::clpalette(4839578)
pal_swatch = colourlovers::swatch(pal)[[1]]
```

It looks like this:

```r
pie(rep(1, length(pal_swatch)), col = pal_swatch)
```

---

### `geom_path()`

To make a parametric figure, eg, of a leaf, you will want to write a function that takes
*  a single vector argument `t`, e.g. on [0, 1]
*  returns a set of `(x,y)` coordinates as a data frame.  
(Consider centering at the origin, and scaling so that its bounding box is `$\pm 1$`).  
*  Then I have provided for you`trans_affine`  which will allow you to scale / rotate / translate the initial figure.

You will need to use some form of iteration to generate a family of parametric figures, then bind the rows, with an identifier showing which 
Below I show a for-loop, but you could also join your unit figure

---
class: code50

```r
source('lab07/affine_trans.R')

# need to include 0 endpoint twice to get a closed path
circle = unit_circle(c(0, ppoints(20), 0))

ellipse_foci = tibble(x = 1:10, y = x^2) %>% rowwise() %>%
  mutate(scale = list(diag(c(sqrt(x), 1 + sqrt(x))))) %>% ungroup()

# collect outputs
ellipse_out = list()
for(ei in seq_len(nrow(ellipse_foci))){
  # current xy center
  xy =  unlist(ellipse_foci[ei, c('x', 'y'), drop = TRUE])
  # current scaling matrix
  scale = ellipse_foci[ei, 'scale', drop = TRUE][[1]]
  # apply trans
  ellipse_out[[ei]] = trans_affine(circle, center = xy, scale = scale)
}

# collect and combine 
ellipses = bind_rows(ellipse_out,
*                    .id = 'figure') # Needed to identify individual closed paths
```

---

```r
ggplot(ellipses, aes(x = x, y = y, group  = figure)) + geom_path()
```

---

```r
ggplot(ellipses, aes(x = x, y = y, group  = figure, fill = as.numeric(figure))) + geom_polygon()
```

---
class: code50

## Branching trees

```r
library(data.tree)

# Need to install development version,
# remotes::install_github("andrewheiss/colourlovers")
library(colourlovers)

bpp = function(parent, level, wind = 0){
    te = rexp(1, rate = 1) + 1
    t = parent$t + te
    branch_span = rt(1, df = 3)*5/level
    branch_center =  parent$x + branch_span + wind
    print(glue::glue("At {level}: t = {t}"))
    if(t > t_max){
      print(glue::glue("At {level}: hit tmax!"))
      return(parent) # hit t_max, stop recursing by returning parent
    }
    n_child = rpois(1, 1.7)
    print(glue::glue("At {level}: t = {t}, n_child = {n_child}"))
    offset = seq(0, to = parent$branch_span/parent$n_sibling, length.out = n_child)
    offset = offset - mean(offset)
    for(level in seq_len(n_child)){
      child = parent$AddChild(level, 
                              t0 = parent$t, t = parent$t + te, te = te, 
                              n_sibling = n_child, 
                              x = branch_center + offset[level], x0 = parent$x,
                              branch_span = branch_span)
      bpp(child, level = level + 1) # add more children
    }
    print(glue::glue("At {level}: added all children!"))
    # added all children, return parent
    return(parent)
}
```

---
class: code50

```r
t_max = 7
t = 0
set.seed(1234)
root = Node$new("Root", t = 0, x = 0, branch_span = 3, n_sibling = 1, te = -1)
```

Let's look at the root:

```r
root
```

```
##   levelName
## 1      Root
```

---

Now grow the tree.

```r
result = bpp(root, level = 1, wind = .4)
```

```
## At 1: t = 3.50175860496223
## At 1: t = 3.50175860496223, n_child = 1
## At 2: t = 4.83392612142473
## At 2: t = 4.83392612142473, n_child = 4
## At 2: t = 6.69633666300655
## At 2: t = 6.69633666300655, n_child = 1
## At 2: t = 8.60025732648524
## At 2: hit tmax!
## At 1: added all children!
## At 3: t = 5.86565165038416
## At 3: t = 5.86565165038416, n_child = 3
## At 2: t = 8.86193031253469
## At 2: hit tmax!
## At 3: t = 7.15846383854011
## At 3: hit tmax!
## At 4: t = 7.60993914679612
## At 4: hit tmax!
## At 3: added all children!
## At 4: t = 5.84179309774175
## At 4: t = 5.84179309774175, n_child = 0
## 
## At 5: t = 6.79580192328871
## At 5: t = 6.79580192328871, n_child = 2
## At 2: t = 11.2210824643022
## At 2: hit tmax!
## At 3: t = 8.36204413059608
## At 3: hit tmax!
## At 2: added all children!
## At 4: added all children!
## At 1: added all children!
```

---

```r
result
```

```
##        levelName
## 1  Root         
## 2   °--1        
## 3       ¦--1    
## 4       ¦   °--1
## 5       ¦--2    
## 6       ¦   ¦--1
## 7       ¦   ¦--2
## 8       ¦   °--3
## 9       ¦--3    
## 10      °--4    
## 11          ¦--1
## 12          °--2
```

---

Convert it into a data frame.  Each row is a node.  The extra arguments are node attributes we want to pull into the data frame

```r
result_frame = ToDataFrameNetwork(result, 'n_sibling', 't', 'te', 'x', 'x0', 't0', 'level')
result_frame
```

```
##        from         to n_sibling        t       te         x
## 1      Root     Root/1         1 3.501759 3.501759 2.0319378
## 2    Root/1   Root/1/1         4 4.833926 1.332168 1.3195197
## 3    Root/1   Root/1/2         4 4.833926 1.332168 1.8634989
## 4    Root/1   Root/1/3         4 4.833926 1.332168 2.4074782
## 5    Root/1   Root/1/4         4 4.833926 1.332168 2.9514575
## 6  Root/1/1 Root/1/1/1         1 6.696337 1.862411 5.6911383
## 7  Root/1/2 Root/1/2/1         3 5.865652 1.031726 1.5481766
## 8  Root/1/2 Root/1/2/2         3 5.865652 1.031726 1.5611205
## 9  Root/1/2 Root/1/2/3         3 5.865652 1.031726 1.5740643
## 10 Root/1/4 Root/1/4/1         2 6.795802 1.961876 0.8153674
## 11 Root/1/4 Root/1/4/2         2 6.795802 1.961876 0.8412551
##          x0       t0 level
## 1  0.000000 0.000000     2
## 2  2.031938 3.501759     3
## 3  2.031938 3.501759     3
## 4  2.031938 3.501759     3
## 5  2.031938 3.501759     3
## 6  1.319520 4.833926     4
## 7  1.863499 4.833926     4
## 8  1.863499 4.833926     4
## 9  1.863499 4.833926     4
## 10 2.951457 4.833926     4
## 11 2.951457 4.833926     4
```

---
class: code50

Final product

```r
palette = sample(clpalettes('top'), 1)[[1]] 
colors = palette %>% swatch %>% .[[1]]

ggplot(result_frame, aes(x = x0, xend = x, y = t0, yend = t, color = t, size = 1/level)) + 
  geom_curve(curvature = .1)  +
  scale_color_gradientn(colors = colors) +
  theme_void() + 
  guides(color = 'none', size = 'none') +
  theme(plot.background = element_rect(fill = 'black'))
```