| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Calculate the region that can be copied from top to bottom."><meta name="keywords" content="rust, rustlang, rust-lang, overlay_bounds"><title>overlay_bounds in image::imageops - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../image/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../image/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><div class="sidebar-elems"><h2><a href="index.html">In image::imageops</a></h2></div></nav><main><div class="width-limiter"><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn">Function <a href="../index.html">image</a>::<wbr><a href="index.html">imageops</a>::<wbr><a class="fn" href="#">overlay_bounds</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="srclink" href="../../src/image/imageops/mod.rs.html#131-146">source</a> · <a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="item-decl"><pre class="rust fn"><code>pub fn overlay_bounds(<br> (bottom_width, bottom_height): (<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>, <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>),<br> (top_width, top_height): (<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>, <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>),<br> x: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>,<br> y: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a><br>) -> (<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>, <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>)</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Calculate the region that can be copied from top to bottom.</p> |
| <p>Given image size of bottom and top image, and a point at which we want to place the top image |
| onto the bottom image, how large can we be? Have to wary of the following issues:</p> |
| <ul> |
| <li>Top might be larger than bottom</li> |
| <li>Overflows in the computation</li> |
| <li>Coordinates could be completely out of bounds</li> |
| </ul> |
| <p>The main idea is to make use of inequalities provided by the nature of <code>saturing_add</code> and |
| <code>saturating_sub</code>. These intrinsically validate that all resulting coordinates will be in bounds |
| for both images.</p> |
| <p>We want that all these coordinate accesses are safe:</p> |
| <ol> |
| <li><code>bottom.get_pixel(x + [0..x_range), y + [0..y_range))</code></li> |
| <li><code>top.get_pixel([0..x_range), [0..y_range))</code></li> |
| </ol> |
| <p>Proof that the function provides the necessary bounds for width. Note that all unaugmented math |
| operations are to be read in standard arithmetic, not integer arithmetic. Since no direct |
| integer arithmetic occurs in the implementation, this is unambiguous.</p> |
| <div class="example-wrap"><pre class="language-text"><code>Three short notes/lemmata: |
| - Iff `(a - b) <= 0` then `a.saturating_sub(b) = 0` |
| - Iff `(a - b) >= 0` then `a.saturating_sub(b) = a - b` |
| - If `a <= c` then `a.saturating_sub(b) <= c.saturating_sub(b)` |
| |
| 1.1 We show that if `bottom_width <= x`, then `x_range = 0` therefore `x + [0..x_range)` is empty. |
| |
| x_range |
| = (top_width.saturating_add(x).min(bottom_width)).saturating_sub(x) |
| <= bottom_width.saturating_sub(x) |
| |
| bottom_width <= x |
| <==> bottom_width - x <= 0 |
| <==> bottom_width.saturating_sub(x) = 0 |
| ==> x_range <= 0 |
| ==> x_range = 0 |
| |
| 1.2 If `x < bottom_width` then `x + x_range < bottom_width` |
| |
| x + x_range |
| <= x + bottom_width.saturating_sub(x) |
| = x + (bottom_width - x) |
| = bottom_width |
| |
| 2. We show that `x_range <= top_width` |
| |
| x_range |
| = (top_width.saturating_add(x).min(bottom_width)).saturating_sub(x) |
| <= top_width.saturating_add(x).saturating_sub(x) |
| <= (top_wdith + x).saturating_sub(x) |
| = top_width (due to `top_width >= 0` and `x >= 0`)</code></pre></div> |
| <p>Proof is the same for height.</p> |
| </div></details></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="image" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
