ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Change of coordinates in Javascript: part 3 in a series

Updated on January 31, 2011
The same line; two different mappings to the screen
The same line; two different mappings to the screen

Comments about Change of Basis

The previous article in this series covered drawing lines in Javascript.  This article adds another tool, mapping of coordinates.

It often comes up that the coordinate system used on your computer screen is not the same as the coordinate system for the problem you are working on.  So, there is frequently an need to map between coordinate systems in order to draw a picture of your problem.

I could have done this by writing a function that takes ten parameters, four to describe the screen coordinates, four to describe the coordinates of my problem, and two to describe the point that I want to map to the screen.  However, I choose instead to store the description of the screen and problem coordinates in an object, and just pass the x and y values of the point I wish to map to a method of that object.

I used the Javascript prototype mechanism to make it possible to base other, similar objects on this one.

In the example, I drew two lines from (-1,-1) to (1,1), but varied the screen coordinates that they map to.  The result is one long line starting in the lower left and rising, which is a more
conventional mapping.  The second line is shorter, starts in the upper left corner and falls to the right, because in this coordinate system greater values of y map to points that are lower on the screen.

I didn't demonstrate it, but changing values of an instance of the jgcoordinates will not change the defaults for subsequent new instances. 

The future examples in my series will make use of coordinate mapping.  If you are interested, I
suggest playing around with this mechanism, some.

example code for changing coordinates in javascript

<html>
<head>
<style type="text/css" >
.whiterectangle { color: white; background-color: white; z-index: 0;}
.blackrectangle { color: black; background-color: black; z-index: 1;}
</style>
<script type="text/javascript" >

var jgpointbase = {
	x: 0,
	y: 0
};

function jgpoint( ) {
	//this.x = x;
	//this.y = y;
};

jgpoint.prototype = jgpointbase;

function jgptsc( x, y ) {
		var rval = new jgpoint( );
		rval.x =  this.screenx0 + (( this.screenx1 - this.screenx0 ) / ( this.x1 - this.x0 )) * ( x - this.x0 );
		rval.y =  this.screeny0 + (( this.screeny1 - this.screeny0 ) / ( this.y1 - this.y0 )) * ( y - this.y0 );
		return( rval );
}

var jgcoordinatesbase = {
	x0: -1.25,
	screenx0: 50,
	y0: -1.25,
	screeny0: 450,
	x1: 1.25,
	screenx1: 450,
	y1: 1.25,
	screeny1: 50,
	pointToScreenCoordinates: jgptsc
};

function jgcoordinates() {
}

jgcoordinates.prototype = jgcoordinatesbase;

function drawrectangle( myclass, top, left, width, height )
{
	var bodylist = document.getElementsByTagName( "body" );
	var rect = document.createElement( "div" );
	var mystyle = 'position:absolute;top:' + top + ";left:" + left + ';width:' + width + ";height:" + height;
	rect.setAttribute( "class", myclass );
	rect.setAttribute( "style", mystyle );
	bodylist[0].appendChild( rect );
}

function drawline( width, x1, y1, x2, y2 )
{
	var x, y, nexty, nextx;

	// ensure x1, y1 is leftmost point
	if( x1 > x2 ) {
		tmp = x2;
		x2 = x1;
		x1 = tmp;
		tmp = y2;
		y2 = y1;
		y1 = tmp;
	}
	var dx = x2 - x1;
	var dy = y2 - y1;

	if( dy == 0 ) { // horizontal line
		drawrectangle( "blackrectangle", y1 - width / 2, x1, dx, width );
		return;
	} else if ( dx == 0 ) { // vertical line
		drawrectangle( "blackrectangle", y1, x1 - width / 2, width, dy );
		return;
	}
	var slope = dy / dx;
	if( slope > 1 || slope < -1 ) {
		// one x per multiple y
		if( y1 < y2 ) {
			y = y1;
			for( x = x1 ; x < x2 ; x += 1 ) {
				nexty = y + slope;
				drawrectangle( "blackrectangle", y, x - width / 2, width, nexty - y );
				y = nexty;
			}
		} else {
			y = y1;
			for( x = x1 ; x < x2 ; x += 1 ) {
				nexty = y + slope;
				drawrectangle( "blackrectangle", nexty, x - width / 2, width, y - nexty );
				y = nexty;
			}
		}

	} else {
		// one y per multiple x
		if( y1 < y2 ){
			x = x1;
			for( y = y1 ; y < y2 ; y += 1 ) {
				nextx = x + 1 / slope;
				drawrectangle( "blackrectangle", y - width / 2, x, nextx - x, width );
				x = nextx;
			}
		} else {
			x = x2;
			for( y = y2 ; y < y1 ; y += 1 ) {
				nextx = x + 1 / slope;
				drawrectangle( "blackrectangle", y - width / 2, nextx, x - nextx, width );
				x = nextx;
			}
		}
	}
		
	
}
</script>
</head>
<body>
<script type="text/javascript" >
drawrectangle( "whiterectangle", 0, 0, "100%", "100%" );  // make a background rectangle, not necessary with default browser settings
var unitsquare = new jgcoordinates();
startpoint = unitsquare.pointToScreenCoordinates( -1, -1 );
endpoint = unitsquare.pointToScreenCoordinates( 1, 1 );
drawline( 4, startpoint.x, startpoint.y, endpoint.x, endpoint.y );
unitsquare.screenx0 = 0;
unitsquare.screeny0 = 0;
unitsquare.screenx1 = 50;
unitsquare.screeny1 = 50;
startpoint = unitsquare.pointToScreenCoordinates( -1, -1 );
endpoint = unitsquare.pointToScreenCoordinates( 1, 1 );
drawline( 4, startpoint.x, startpoint.y, endpoint.x, endpoint.y );

</script>
</body>
</html>

Comments

    0 of 8192 characters used
    Post Comment

    No comments yet.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)