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<!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="API documentation for the Rust `overlay_bounds` fn in crate `image`."><meta name="keywords" content="rust, rustlang, rust-lang, overlay_bounds"><title>image::imageops::overlay_bounds - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc fn"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../image/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><div class="sidebar-elems"><p class='location'><a href='../index.html'>image</a>::<wbr><a href='index.html'>imageops</a></p><script>window.sidebarCurrent = {name: 'overlay_bounds', ty: 'fn', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../../src/image/imageops/mod.rs.html#102-117' title='goto source code'>[src]</a></span><span class='in-band'>Function <a href='../index.html'>image</a>::<wbr><a href='index.html'>imageops</a>::<wbr><a class="fn" href=''>overlay_bounds</a></span></h1><pre class='rust fn'>pub fn overlay_bounds(<br> (bottom_width, bottom_height): <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><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><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>, <br> (top_width, top_height): <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><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><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</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.tuple.html">(</a><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><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></pre><div class='docblock'><p>Calculate the region that can be copied from top to bottom.</p>
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<p>Given image size of bottom and top image, and a point at which we want to place the top image
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onto the bottom image, how large can we be? Have to wary of the following issues:</p>
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<ul>
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<li>Top might be larger than bottom</li>
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<li>Overflows in the computation</li>
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<li>Coordinates could be completely out of bounds</li>
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</ul>
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<p>The main idea is to make use of inequalities provided by the nature of <code>saturing_add</code> and
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<code>saturating_sub</code>. These intrinsically validate that all resulting coordinates will be in bounds
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for both images.</p>
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<p>We want that all these coordinate accesses are safe:</p>
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<ol>
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<li><code>bottom.get_pixel(x + [0..x_range), y + [0..y_range))</code></li>
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<li><code>top.get_pixel([0..x_range), [0..y_range))</code></li>
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</ol>
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<p>Proof that the function provides the necessary bounds for width. Note that all unaugmented math
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operations are to be read in standard arithmetic, not integer arithmetic. Since no direct
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integer arithmetic occurs in the implementation, this is unambiguous.</p>
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<pre><code class="language-text">Three short notes/lemmata:
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- Iff `(a - b) <= 0` then `a.saturating_sub(b) = 0`
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- Iff `(a - b) >= 0` then `a.saturating_sub(b) = a - b`
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- If `a <= c` then `a.saturating_sub(b) <= c.saturating_sub(b)`
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1.1 We show that if `bottom_width <= x`, then `x_range = 0` therefore `x + [0..x_range)` is empty.
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x_range
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= (top_width.saturating_add(x).min(bottom_width)).saturating_sub(x)
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<= bottom_width.saturating_sub(x)
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bottom_width <= x
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<==> bottom_width - x <= 0
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<==> bottom_width.saturating_sub(x) = 0
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==> x_range <= 0
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==> x_range = 0
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1.2 If `x < bottom_width` then `x + x_range < bottom_width`
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x + x_range
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<= x + bottom_width.saturating_sub(x)
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= x + (bottom_width - x)
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= bottom_width
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2. We show that `x_range <= top_width`
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x_range
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= (top_width.saturating_add(x).min(bottom_width)).saturating_sub(x)
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<= top_width.saturating_add(x).saturating_sub(x)
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<= (top_wdith + x).saturating_sub(x)
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= top_width (due to `top_width >= 0` and `x >= 0`)
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</code></pre>
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<p>Proof is the same for height.</p>
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