Fastest path to cover area
$begingroup$
How do we determine the fastest path to cover an area using an object of some radius r? E.g. a machine that needs to spray a chemical onto a surface. I assume this is some kind of NP-hard problem.
approximation np-complete
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
$endgroup$
add a comment |
$begingroup$
How do we determine the fastest path to cover an area using an object of some radius r? E.g. a machine that needs to spray a chemical onto a surface. I assume this is some kind of NP-hard problem.
approximation np-complete
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
$endgroup$
add a comment |
$begingroup$
How do we determine the fastest path to cover an area using an object of some radius r? E.g. a machine that needs to spray a chemical onto a surface. I assume this is some kind of NP-hard problem.
approximation np-complete
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
$endgroup$
How do we determine the fastest path to cover an area using an object of some radius r? E.g. a machine that needs to spray a chemical onto a surface. I assume this is some kind of NP-hard problem.
approximation np-complete
approximation np-complete
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
edited Dec 22 '18 at 14:34
Paul Frost
10.3k3933
10.3k3933
asked Sep 6 '13 at 12:58
user93433user93433
1
asked Sep 6 '13 at 12:58
user93433user93433
1
asked Sep 6 '13 at 12:58
user93433user93433
1
1
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f485716%2ffastest-path-to-cover-area%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
$endgroup$
add a comment |
$begingroup$
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
$endgroup$
add a comment |
$begingroup$
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
$endgroup$
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
edited Sep 6 '13 at 15:11
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
answered Sep 6 '13 at 14:21
bubbabubba
30.4k33086
30.4k33086
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f485716%2ffastest-path-to-cover-area%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
