---
title: "Areal Interpolation"
date: "`r Sys.Date()`"
code-annotations: hover
urlcolor: blue
vignette: >
  %\VignetteIndexEntry{Areal Interpolation}
  %\VignetteEngine{quarto::html}
  %\VignetteEncoding{UTF-8}
knitr:
  opts_chunk:
    collapse: true
    comment: "#>"
    out.width: "100%"
---

```{r}
#| include: false

# CRAN OMP THREAD LIMIT to avoid CRAN NOTE
Sys.setenv(OMP_THREAD_LIMIT = 2)
```

This vignette demonstrates how to use `ddbs_interpolate_aw()` to perform areal-weighted interpolation. This technique is essential when you need to transfer attributes from one set of polygons (source) to another incongruent set of polygons (target) based on their area of overlap.

`ddbs_interpolate_aw()` can be 9-30x faster than `sf::st_interpolate_aw` or [`areal::aw_interpolate`](https://chris-prener.github.io/areal/reference/aw_interpolate.html) (see benchmarks in [`{ducksf}`](https://www.ekotov.pro/ducksf/){target="_blank"} where prototype of `ddbs_interpolate_aw()` was originally developed).

`duckspatial` handles these heavy geometric calculations efficiently using DuckDB. We will cover three scenarios:

1.  **Extensive vs. Intensive**: Understanding the difference between mass-preserving counts and densities.
2.  **Fast Output**: Returning a `tibble` (no geometry) for maximum speed.
3.  **Database Mode**: Performing operations on persistent database tables.

### Setup Data

We will use the North Carolina dataset from the `sf` package as our **source**, and create a generic grid as our **target**. 

*Note: We project the data to Albers Equal Area (EPSG:5070) because accurate interpolation requires an equal-area projection.*

```{r}
#| label: setup
#| message: false
#| warning: false
library(duckspatial)
library(sf)

# 1. Load Source Data (NC Counties)
nc <- st_read(system.file("shape/nc.shp", package = "sf"), quiet = TRUE)

# 2. Transform to projected CRS (Albers) for accurate area calculations
nc <- st_transform(nc, 5070)

# 3. Create a Target Grid
grid <- st_make_grid(nc, n = c(10, 5)) |> st_as_sf()

# 4. Create Unique IDs (Required for interpolation)
nc$source_id <- 1:nrow(nc)
grid$target_id <- 1:nrow(grid)
```

## 1) Extensive vs. Intensive Interpolation

Areal interpolation works differently depending on the nature of the data.

### Case A: Extensive Variables (Counts)
Variables like population counts or total births (`BIR74`) are **spatially extensive**. If a source polygon is split in half, the count should also be split in half. We use `weight = "total"` to ensure strict mass preservation relative to the source.

```{r}
# Interpolate Total Births (Extensive)
res_extensive <- ddbs_interpolate_aw(
  target = grid,
  source = nc,
  tid = "target_id",
  sid = "source_id",
  extensive = "BIR74",
  weight = "total",
  mode = "sf"
)
```

**Verification:** The total sum of births in the result should match the original data (mass preservation).

```{r}
orig_sum <- sum(nc$BIR74)
new_sum  <- sum(res_extensive$BIR74, na.rm = TRUE)

sprintf("Original: %s | Interpolated: %s", orig_sum, round(new_sum, 1))
```

### Case B: Intensive Variables (Densities/Ratios)
Variables like population density or infection rates are **spatially intensive**. If a source polygon is split, the density remains the same in both pieces. `duckspatial` handles this by calculating the area-weighted average.

```{r}
# Interpolate 'BIR74' treating it as an intensive variable (e.g. density assumption)
res_intensive <- ddbs_interpolate_aw(
  target = grid,
  source = nc,
  tid = "target_id",
  sid = "source_id",
  intensive = "BIR74", # Treated as density here
  weight = "sum",      # Standard behavior for intensive vars
  mode = "sf"
)
```

### Visual Comparison

Notice the difference in patterns. Extensive interpolation accumulates values based on how much "stuff" falls into a grid cell, while intensive interpolation smoothes the values based on overlap.

```{r, fig.height=5, fig.width=7}
# Combine for plotting
plot_data <- res_extensive[, "BIR74"]
names(plot_data)[1] <- "Extensive_Count"
plot_data$Intensive_Value <- res_intensive$BIR74

plot(plot_data[c("Extensive_Count", "Intensive_Value")], 
     main = "Interpolation Methods Comparison",
     border = "grey90",
     key.pos = 4)
```

## 2) High Performance: Output as Tibble

If you are working with massive datasets, constructing the geometry for the result `sf` object can be slow. If you only need the interpolated numbers, collect the default `duckspatial_df` using `ddbs_collect(as = "tibble")`. This skips the geometry construction step and is significantly faster.

```{r}
# Return a standard data.frame/tibble without geometry
res_tbl <- ddbs_interpolate_aw(
  target = grid,
  source = nc,
  tid = "target_id",
  sid = "source_id",
  extensive = "BIR74"
) |> 
  ddbs_collect(as = "tibble")

head(res_tbl)
```

## 3) Database Mode: Large Data Workflows

For datasets larger than memory, or for persistent pipelines, you can perform the interpolation directly inside the DuckDB database without pulling data into R until the end.

First, let's establish a connection and load our spatial layers into tables.

```{r}
# Create connection
conn <- ddbs_create_conn()

# Write layers to DuckDB
ddbs_write_vector(conn, nc, "nc_table", overwrite = TRUE)
ddbs_write_vector(conn, grid, "grid_table", overwrite = TRUE)
```

Now we run the interpolation by referencing the table names. We can also use the `name` argument to save the result directly to a new table instead of returning it to R.

```{r}
# Run interpolation and save to new table 'nc_grid_births'
ddbs_interpolate_aw(
  conn = conn,
  target = "grid_table",
  source = "nc_table",
  tid = "target_id",
  sid = "source_id",
  extensive = "BIR74",
  weight = "total",
  name = "nc_grid_births", # <--- Writes to DB
  overwrite = TRUE
)

# Verify the table was created
DBI::dbListTables(conn)
```

We can now query this table or read it back later.

```{r}
# Read the result back from the database
final_sf <- ddbs_read_vector(conn, "nc_grid_births")

head(final_sf)
```

If we only wanted the database table, without the geometry, we could do:

```{r}
ddbs_interpolate_aw(
  conn = conn,
  target = "grid_table",
  source = "nc_table",
  tid = "target_id",
  sid = "source_id",
  extensive = "BIR74",
  weight = "total",
  name = "nc_grid_births", # <--- Writes to DB
  overwrite = TRUE,
  mode = "tibble"
)
```

And preview this table directly in the database:

```{r}
as_duckspatial_df("nc_grid_births", conn)
```

### Cleanup

Always close the connection when finished.

```{r}
duckdb::dbDisconnect(conn)
```
