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  • Mac vs. Windows Browser Font Height Rendering Issue

    - by cdmckay
    I'm using a custom font and the @font-face tag. In Windows, everything looks great, regardless of whether it's Firefox, Chrome, or IE. On Mac, it's a different story. For some reason, the Mac font renderer thinks the font is a lot shorter than it is. For example, consider this test code (live example here): <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <title>Webble</title> <style type="text/css"> @font-face { font-family: "Bubbleboy 2"; src: url("bubbleboy-2.ttf") format('truetype'); } body { font-family: "Bubbleboy 2"; font-size: 30px; } div { background-color: maroon; color: yellow; height: 100px; line-height: 100px; } </style> </head> <body> <div>The quick brown fox jumped over the lazy dog.</div> </body> </html> Open it on Windows Firefox and on Mac Firefox. Use your mouse to select it. On Windows, you'll notice it fully selects the font. On Mac, it only selects about half the font. If you look at what it is selecting, you'll see that that part has been centered, instead of the full height of the font. Is there anyway to fix this rather large discrepancy?

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  • Reverse rendering of Urdu fonts

    - by Syed Muhammad Umair
    I am working on a project that is based on Urdu language in Ubuntu platform. I'm using Python language and have almost achieved my task. The problem is that, the Urdu text is rendered in reverse order. For example, consider the word ??? (which means work) consisting of the three letters: ? , ? , and ? The output is rendered in reverse order as ??? consisting of the three letters: ?, ?, and ? When copying this text to Open Office or opening the generated XML file in Firefox, the generated result is absolutely desired. I Am using Python 2.6 IDLE, its working perfect with Windows platform, which clearly shows its not the problem of IDLE. Am working on TKINTER GUI library. How can this problem be solved?

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  • JPanel: both implementing my own paintComponent() and rendering children doesn't work

    - by Paul Marshall
    I'm extending a JPanel to display a game board, and adding a JEditorPane at the bottom to hold some status text. Unfortunately, the game board renders just fine, but the JEditorPane is just a blank gray area until I highlight the text in it, when it will render whatever text is highlighted (but not the rest). If I'm understanding Swing right, it should work, because super.paintComponent(g) should render the other children (i.e., the JEditorPane). Tell me, o great stackoverflow, what bonehead mistake am I making? public GameMap extends JPanel { public GameMap() { JEditorPane statusLines = new JEditorPane("text/plain","Stuff"); this.setLayout(new BoxLayout(this,BoxLayout.PAGE_AXIS)); this.add(new Box.Filler(/*enough room to draw my game board*/)); this.add(statusLines); } public void paintComponent(Graphics g){ super.paintComponent(g); for ( all rows ){ for (all columns){ //paint one tile } } } }

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  • fullCalendar not rendering new events dynamically

    - by morpheous
    I have the following code in a page on which I am using fullCalendar. I am able to add events in my page, however the calendar does not display this dynamically. I have to move to another month (and then back to the current month), before the dates I added are displayed. Is there a way to dynamically refresh/render the calendar as dates are programatically added to it? Here is a snippet of my code so far: ## the code for generating the calendar <script> $(document).ready(function() { $('#calendar').fullCalendar({ editable: false, events: 'http://example.com/getevents.php', }); }); </script> <h1>Calendar Test</h1> <div id='calendar'></div> ## the code for updating it $('#calendar').fullCalendar( 'refetchEvents' );

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  • Browser dependent problem rendering WMD with Showdown.js?

    - by CMPalmer
    This should be easy (at least no one else seems to be having a similar problem), but I can't see where it is breaking. I'm storing Markdown'ed text in a database that is entered on a page in my app. The text is entered using WMD and the live preview looks correct. On another page, I'm retrieving the markdown text and using Showdown.js to convert it back to HTML client-side for display. Let's say I have this text: The quick **brown** fox jumped over the *lazy* dogs. 1. one 1. two 4. three 17. four I'm using this snippet of Javascript in my jQuery document ready event to convert it: var sd = new Attacklab.showdown.converter(); $(".ClassOfThingsIWantConverted").each(function() { this.innerHTML = sd.makeHtml($(this).html()); } I suspect this is where my problem is, but it almost works. In FireFox, I get what I expected: The quick brown fox jumped over the lazy dogs. one two three four But in IE (7 and 6), I get this: The quick brown fox jumped over the lazy dogs. 1. one 1. two 4. three 17. four So apparently, IE is stripping the breaks in my markdown code and just converting them to spaces. When I do a view source of the original code (prior to the script running), the breaks are there inside the container DIV. What am I doing wrong? UPDATE It is caused by the IE innerHTML/innerText "quirk" and I should have mentioned before that this one on an ASP.Net page using data bound controls - there are obviously a lot of different workarounds otherwise.

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  • Calculating 2D angles for 3D objects in perspective

    - by Will
    Imagine a photo, with the face of a building marked out. Its given that the face of the building is a rectangle, with 90 degree corners. However, because its a photo, perspective will be involved and the parallel edges of the face will converge on the horizon. With such a rectangle, is it possible to calculate the angle in 2D of the edges of a face that is 90 degrees to it? In the image below, the blue is the face marked on the photo, and I'm wondering how to calculate the 2D vector of the red lines of the other face:

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  • IE not rendering div contents

    - by The.Anti.9
    I've written an app using HTML 5 and I wan't to show an error box instead of the page when someone visits from IE. When it detects navigator.appName as Microsoft Internet Explorer it hides everything and shows the error div that started out hidden. The div is as follows: <div id='ieerror' style='display:none;width:500px;height:500px;border:3px solid #ff0000;position:absolute;top:50%;left:50%;margin-top:-250px;margin-left:-250px;'> <center> <h1 style='font-size: 30px;'>Internet Explorer is not supported by Aud!</h1><br /><br /> <p>Internet Explorer does not support HTML 5 and therefore this application cannot run.<br /> Please upgrade your browser. We suggest <a href='http://www.google.com/chrome'>Google Chrome</a>!</p> </center> </div> The problem is that when I visit the page in IE, the div pops up with the border, but it has no contents. Nothing is inside of it. I went to view->source and looked at it, and the code is still there, but none of it is rendered. How do I fix this?

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  • CSS not rendering on MAMP

    - by Debashis
    I'm working on a Wordpress blog. I'm embedding a stylesheet as follows: <link rel=”stylesheet” href="<?php bloginfo("stylesheet_url"); ?>" type=”text/css” media=”screen” /> However, the CSS doesn't render, at all. I've checked that the URL that is being put in the href is correct. The CSS is found. But, it doesn't render, in all browsers. I am utterly stumped, and would really appreciate a nudge in the right direction. I'm using MAMP 1.8.3, and Wordpress 1.2.9.

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  • Collision point of 2 curves in a 3d-room

    - by Frank
    Hello, i am programming a small game for quite some time. We started coding a small FPS-Shooter inside of a project at school to get a bit experience using directX. I dont know why, but i couldnt stop the project and started programming at home aswell. At the moment i am trying to create some small AI. Of cause thats definatlly not easy, but thats my personal goal anyways. The topic could prolly fill multiple books hehe. I've got the walking part of my bots done so far. They walk along a scriped path. I am not working on the "aiming" of the bots. While programming that i hit on some math problem i couldnt solve yet. I hope of your input on this to help me get further. Concepts, ideas and everything else are highly appreciated. Problem: Calculate the position (D3DXVECTOR3) where the curve of the projectile (depends on gravity, speed), hit the curved of the enemys walking path (depends on speed). We assume that the enemy walks in a constant line. Known variables: float projectilSpeed = 2000 m/s //speed of the projectile per second float gravitation = 9.81 m/s^2 //of cause the gravity lol D3DXVECTOR3 targetPosition //position of the target stored in a vector (x,y,z) D3DXVECTOR3 projectilePosition //position of the projectile D3DXVECTOR3 targetSpeed //stores the change of the targets position in the last second Variabledefinition ProjectilePosition at time of collision = ProjectilePos_t TargetPosition at time of collision = TargetPos_t ProjectilePosition at time 0, now = ProjectilePos_0 TargetPosition at time 0, now = TargetPos_0 Time to impact = t Aim-angle = theta My try: Found a formular to calculate "drop" (Drop of the projectile based on the gravity) on Wikipedia: float drop = 0.5f * gravity * t * t The speed of the projectile has a horizontal and a vertical part.. Found a formular for that on wikipedia aswell: ProjectilVelocity.x = projectilSpeed * cos(theta) ProjectilVelocity.y = projectilSpeed * sin(theta) So i would assume this is true for the projectile curve: ProjectilePos_t.x = ProjectilePos_0.x + ProjectileSpeed * t ProjectilePos_t.y = ProjectilePos_0.y + ProjectileSpeed * t + 0.5f * gravity * t * t ProjectilePos_t.z = ProjectilePos_0.z + ProjectileSpeed * t The target walk with a constant speed, so we can determine his curve by this: TargetPos_t = TargetPos_0 + TargetSpeed * D3DXVECTOR3(t, t, t) Now i dont know how to continue. I have to solve it somehow to get a hold on the time to impact somehow. As a basic formular i could use: float time = distanz / projectileSpeed But that wouldnt be truly correct as it would assume a linear "Trajectory". We just find this behaivor when using a rocket. I hope i was able to explain the problem as much as possible. If there are questions left, feel free to ask me! Greets from germany, Frank

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  • Can 3D OpenGL game written in Python look good and run fast?

    - by praavDa
    I am planning to write an simple 3d(isometric view) game in Java using jMonkeyEngine - nothing to fancy, I just want to learn something about OpenGL and writing efficient algorithms (random map generating ones). When I was planning what to do, I started wondering about switching to Python. I know that Python didn't come into existence to be a tool to write 3d games, but is it possible to write good looking games with this language? I have in mind 3d graphics, nice effects and free CPU time to power to rest of game engine? I had seen good looking java games - and too be honest, I was rather shocked when I saw level of detail achieved in Runescape HD. On the other hand, pygame.org has only 2d games, with some starting 3d projects. Are there any efficient 3d game engines for python? Is pyopengl the only alternative? Good looking games in python aren't popular or possible to achieve? I would be grateful for any information / feedback.

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  • Adding additional components to a web page after rendering by Wicket

    - by Andrew Fielden
    I have a requirement to create a web page using Wicket 1.5, which can present a variable number of panels to capture user input. All the panels have the same structure. The page would start off with one panel, and includes a button to dynamically add more as required. So the number of panels is unknown at the time the page is initially rendered. Effectively I'd be altering the structure of the page dynamically. This is possible in Javascript, using document.addElement() I've done a similar thing in the past by creating all the components on page load, and selectively showing/hiding components. The difference here is that the number of components (panels) is initially unknown. I'm unsure as to how this would be achieved with Wicket.

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  • CALayer and Off-Screen Rendering

    - by Luke Mcneice
    I have a Paging UIScrollView with a contentSize large enough to hold a number of small UIScrollViews for zooming, The viewForZoomingInScrollView is a viewController that holds a CALayer for drawing a PDF page onto. This allows me to navigate through a PDF much like the ibooks PDF reader. The code that draws the PDF (Tiled Layers) is located in: - (void)drawLayer:(CALayer *)layer inContext:(CGContextRef)ctx; And simply adding a 'page' to the visible screen calls this method automatically. When I change page there is some delay before all the tiles are drawn, even though the object (page) has already been created. What i want to be able to do is render the next page before the user scrolls to it, thus preventing the visible tiling effect. However, i have found that if the layer is located offscreen adding it to the scrollview doesn't call the drawLayer. Any Ideas/common gotchas here? I have tried: [viewController.view.layer setNeedsLayout]; [viewController.view.layer setNeedsDisplay]; NB: The fact that this is replicating the ibooks functionally is irrelevant within the context of the full app.

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  • Pango Cursor Rendering and Highlighting....

    - by user367255
    How do you render the cursor and create highlighting for selected text in Pango? Also, can I use PangoCairo to render parts of a layout at a time, so I can draw it in different ways (such as with an outline)? Finally, how did you get your understanding of Pango, there doesn't seem to be very many tutorials and the technical documentation only describes the functions. Thanks!

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  • rendering specific fields with Rails

    - by Tam
    Hi, If I have an object say @user and I want to render only certain fields in it say first_name and last_name(I'm using AMF) render :amf => @user how do I do that? I know I can use :select when doing the 'find' but I need to use the other field at the server side but don't want to send them with AMF to the client side and I don't want to do a second 'find' Thanks, Tam

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  • Codeigniter - form not rendering on live server?

    - by pingu
    hi guys, I've written a small website with CI, which is all working fine on dev. However, when I copy the files over for live, everything works except for my form which is not being rendered. I am using <?php echo form_open('home'); ?> and <?php echo form_close(); ?> The form fields within the form, which I'm generating as follows are being rendered fine, but there is simply no form around them?! <?php $data = array( 'name'=> 'name', 'id'=> 'name', 'class'=>'textfield', 'value' => set_value('name') ); echo form_input($data); ?> Any ideas - I've used CI on a few apps, and this is the first time I've come across this issue. I've got all the helpers etc called correctly, as this is working perfectly in the development environment.

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  • Dojo and Ajax - rendering widgets

    - by Michael Merchant
    I'm trying to load content into a Dojo content pane in a specific html tag and not replace the entire content pane. The html I'm loading includes a markup defined widget that I'd like to have rendered when the new row is loaded. So, I have a table that is being dynamically filled via ajax,ie: <body> <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/dojo/1.5/dojo/dojo.xd.js" djConfig="parseOnLoad: true, isDebug:true"></script> <div id="table-pane" dojoType="dijit.layout.ContentPane"> <table class="test"> <tbody> <tr><td>Name</td><td>Year</td><td>Age</td></tr> <tr> <td><span dojoType="dijit.InlineEditBox" editor="dijit.form.Textarea">Mike</span> </td> <td>2010</td> <td>12</td> </tr> </tbody> </table> </div> </body> <script> var html ='<tr><td><span dojoType="dijit.InlineEditBox" editor="dijit.form.Textarea">John</span></td><td>2011</td><td>22</td></tr>'; dojo.require("dijit.layout.ContentPane"); dojo.require("dijit.InlineEditBox"); dojo.require("dijit.form.Textarea"); dojo.addOnLoad(function(){ pane = dijit.byId("table-pane"); add_elem(); }); function add_elem(){ var node = $(".test tr:last"); node.after(html); dojo.addOnLoad(function(){ //Here I want to initiate any widgets that haven't been initiated pane.buildRendering(); }); }</script> How do I render the Dojo widget in the new table row?

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  • matlab image processing 3d

    - by jaysean
    i have 100 b&w image of smthing.the probllem is i want to scan each image in 0&1 formatin mby n format and then place each image to one over one and again scan and save them in mbynby100 form. how i do this and from where i should start _jaysean

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  • Rendering of graphics different depending on DisplayObject position

    - by jedierikb
    When drawing vertical lines with a non-integer x-value (e.g., 1.75) to a sprite, the lines are drawn differently based on the non-integer x-value of the sprite. In the picture below are two pairs of very close together vertical lines. As you can see, they look very different. This is frustrating, especially when animating the sprite. Any ideas how ensure that sprites-with-non-integer-positions' graphics will visually display the same way regardless of the sprite position? package { import flash.display.Sprite; import flash.display.StageAlign; import flash.display.StageScaleMode; import flash.events.Event; public class tmp extends Sprite { private var _sp1:Sprite; private var _sp2:Sprite; public function tmp( ):void { stage.align = StageAlign.TOP_LEFT; stage.scaleMode = StageScaleMode.NO_SCALE; _sp1 = new Sprite( ); drawButt( _sp1 ); _sp1.x = 100; _sp1.y = 100; _sp2 = new Sprite( ); drawButt( _sp2 ); _sp2.x = 100; _sp2.y = 200; addChild( _sp1 ); addChild( _sp2 ); addEventListener( Event.ENTER_FRAME, efCb, false, 0, true ); } private function efCb( evt:Event ):void { var nx:Number = _sp2.x + .1; if (nx > 400) { nx = 100; } _sp2.x = nx; } private function drawButt( sp:Sprite ):void { sp.graphics.clear( ); sp.graphics.lineStyle( 1, 0, 1, true ); sp.graphics.moveTo( 1, 1 ); sp.graphics.lineTo( 1, 100 ); sp.graphics.lineStyle( 1, 0, 1, true ); sp.graphics.moveTo( 1.75, 1 ); sp.graphics.lineTo( 1.75, 100 ); } } }

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  • rendering front-end of survey into an MVC app

    - by HotKey
    Lately I have been watching Pluralsight intro videos on MVC 3. I have never worked with the Model View Control approach before, but I'm starting to understand how these 3 crucial parts of an app are separated. I created a front-end prototype of a survey I would like to implement into a View of my MVC web app. The survey is in HTML, CSS, using jQuery to deliver content changes depending on the type of evaluation (6-11 questions), and jQuery UI for a couple slider ratings. I noticed through tutorials that you can use an HTML form and helpers that allow the user to edit content, but my prototype already allows the users to rate via radio buttons, comment text boxes, and sliders. Would I need to change any of my existing code if I just want to store this employee data to the Model, and depending on what survey's the employee has completed through the Controller, disable drop down fields? Also, would I store the current employee data on submit of survey through an HttpPost in the Controller to the Model? My apologies if my questions seem rather vague. Could someone point me in the right direction to a resource or documentation similar to my needs above? The Pluralsight videos are taking me in the wrong direction.

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  • Inline-SVG not rendering when generated by JS

    - by Lucas Gasenzer
    I want to implement some visual statistics into a jQuery mobile page. If I embed the folowing snippet it will show me the same results as if I would embed it from a separate *.svg-file. <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" height="115" width="100%"> <rect x="0%" y="0" fill="#8cc63f" width="19.2%" height="100" /> <text x="10%" y="115" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">A</text> <text x="10%" y="15" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">100</text> <rect x="20.2%" y="50" fill="#8cc63f" width="19.2%" height="50" /> <text x="30.2%" y="115" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">B</text> <text x="30.2%" y="65" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">50</text> <rect x="40.4%" y="90" fill="#8cc63f" width="19.2%" height="10" /> <text x="50.4%" y="115" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">C</text> <text x="50.4%" y="85" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">10</text> <rect x="60.6%" y="78" fill="#8cc63f" width="19.2%" height="22" /> <text x="70.6%" y="115" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">D</text> <text x="70.6%" y="73" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">22</text> <rect x="80.8%" y="40" fill="#8cc63f" width="19.2%" height="60" /> <text x="90.8%" y="115" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">E</text> <text x="90.8%" y="55" font-family="helvetica, sans-serif" font-size="10" style="text-anchor:middle;">60</text> Now because these statistics obviously change for each site I generate code like the one above using JavaScript. The HTML-Source-Code looks the same but the SVG will not be showing. Instead it looks like this: A 100 B 50 C 10 D 22 E60 so really just a line of text Am I missing something? Thank you for your help!

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  • ASP.NET Rendering XMl/XSLT direct from the web - problem with non virtual path

    - by H4mm3rHead
    Hi, i have a small problem. Im using the ASP.NET Xml control and want to pass it a url to a rss feed and a stylesheet - so that i can style the rss myself on my website. When applying the full web path to the xml control (http://www.myserver.com/myfeed.rss) i get an exception telling me that the document source is not a valid virtual path. What am i doing wrong? I would hate to download the file before showing it...

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  • Pygame Sprite/Font rendering issues

    - by Grimless
    Hey guys. Here's my problem: I have a game class that maintains a HUD overlay that has a bunch of elements, including header and footer background sprites. Everything was working fine until I added a 1024x128 footer sprite. Now two of my text labels will not render, despite the fact that they DO exist in my Group and self.elements array. Is there something I'm missing? When I take out the footerHUDImage line, all of the labels render correctly and everything works fine. When I add the footerHUDImage, two of the labels (the first two) no longer render and the third only sometimes renders. HELP PLEASE! Here is the code: class AoWHUD (object): def __init__(self, screen, delegate, dataSource): self.delegate = delegate self.dataSource = dataSource self.elements = [] headerHudImage = KJRImage("HUDBackground.png") self.elements.append(headerHudImage) headerHudImage.userInteractionEnabled = True footerHUDImage = KJRImage("ControlsBackground.png") self.elements.append(footerHUDImage) footerHUDImage.rect.bottom = screen.get_rect().height footerHUDImage.userInteractionEnabled = True lumberMessage = "Lumber: " + str(self.dataSource.lumber) lumberLabel = KJRLabel(lumberMessage, size = 48, color = (240, 200, 10)) lumberLabel.rect.topleft = (_kSpacingMultiple * 0, 0) self.elements.append(lumberLabel) stoneMessage = "Stone: " + str(self.dataSource.stone) stoneLabel = KJRLabel(stoneMessage, size = 48, color = (240, 200, 10)) stoneLabel.rect.topleft = (_kSpacingMultiple * 1, 0) self.elements.append(stoneLabel) metalMessage = "Metal: " + str(self.dataSource.metal) metalLabel = KJRLabel(metalMessage, size = 48, color = (240, 200, 10)) metalLabel.rect.topleft = (_kSpacingMultiple * 2, 0) self.elements.append(metalLabel) foodMessage = "Food: " + str(len(self.dataSource.units)) + "/" + str(self.dataSource.food) foodLabel = KJRLabel(foodMessage, size = 48, color = (240, 200, 10)) foodLabel.rect.topleft = (_kSpacingMultiple * 3, 0) self.elements.append(foodLabel) self.selectionSprites = {32 : pygame.image.load("Selected32.png").convert_alpha(), 64 : pygame.image.load("Selected64.png")} self._sprites_ = pygame.sprite.Group() for e in self.elements: self._sprites_.add(e) print self.elements def draw(self, screen): if self.dataSource.resourcesChanged: lumberMessage = "Lumber: " + str(self.dataSource.lumber) stoneMessage = "Stone: " + str(self.dataSource.stone) metalMessage = "Metal: " + str(self.dataSource.metal) foodMessage = "Food: " + str(len(self.dataSource.units)) + "/" + str(self.dataSource.food) self.elements[2].setText(lumberMessage) self.elements[2].rect.topleft = (_kSpacingMultiple * 0, 0) self.elements[3].setText(stoneMessage) self.elements[3].rect.topleft = (_kSpacingMultiple * 1, 0) self.elements[4].setText(metalMessage) self.elements[4].rect.topleft = (_kSpacingMultiple * 2, 0) self.elements[5].setText(foodMessage) self.elements[5].rect.topleft = (_kSpacingMultiple * 3, 0) self.dataSource.resourcesChanged = False self._sprites_.draw(screen) if self.delegate.selectedUnit: theSelectionSprite = self.selectionSprites[self.delegate.selectedUnit.rect.width] screen.blit(theSelectionSprite, self.delegate.selectedUnit.rect)

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  • iPad/iPhone Dev: displayViewController Is Rendering Portrait in Landscape Orientation

    - by Holly
    -(void)displayFirstScreen { UIViewController *displayViewController=[[UIViewController alloc] init]; displayViewController.view = displaySplash; [self presentModalViewController:displayViewController animated:NO]; [self performSelector:@selector(removeScreen) withObject:nil afterDelay:2.0]; [displayViewController release]; } -(void)removeScreen { [[self modalViewController] dismissModalViewControllerAnimated:YES]; } The above code works but my orientation is landscape and the view comes and goes in portrait. Any ideas? Thanks in advance!

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  • 3D Math: Calculate Bank (Roll) angle from Look and Up orthogonal vectors

    - by 742
    I hope this is the proper location to ask this question which is the same as this one, but expressed as pure math instead of graphically (at least I hope I translated the problem to math correctly). Considering: two vectors that are orthogonal: Up (ux, uy, uz) and Look (lx, ly, lz) a plane P which is perpendicular to Look (hence including Up) Y1 which is the projection of Y (vertical axis) along Look onto P Question: what is the value of the angle between Y1 and Up? As mathematicians will agree, this is a very basic question, but I've been scratching my head for at least two weeks without being able to visualize how to project Y onto P... maybe now too old for finding solutions to school exercises. I'm looking for the trigonometric solution, not a solution using a matrix. Thanks.

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