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How to make website scroll with the background not moving and toolbar automatically minimize?

Is there a JS for these features or how actually does it works? (Please check out the sites below)
As the user scrolls down the top toolbar minimizes and remains at the top. Also the pictures seems not to move with the scroll...
Thanks!
http://getflywheel.com/
http://www.google.com/nexus/7/

For the first example you have to set the position:fixed attribute on css for your background. An eventhandler must be check if the user had reached the bottom to display the toolbar on top of the page.
In the second example there is no fixed background but a parallanxed background here is a good example.

position:fixed for toolbar.
In first example also event handler for JS onscroll event, where check if user scrolled
enough to show toolbar

Can I show the scrollbar on iPad even when I'm not scrolling?

I'm using "-webkit-overflow-scrolling": "touch" to show the scrollbar on a scrollable element on iPad.
The scroll button appears only when i'm touching the screen but I would like to be permanently visible so the user can see that there is more content.
Any suggestions?

There is no function available to make scrollbar permanently visible. But if you want to implement some thing like this, you should customize this using delegate function for UIScrollView.
Doc: http://developer.apple.com/library/ios/#documentation/uikit/reference/UIScrollView_Class/Reference/UIScrollView.html

Scrolling a div vertically using buttons

I'm building a mobile app using HTML, CSS, Javascript and jQuery.
Is there a way to scroll a div that is longer (700px) than the mobile screen (480px) using only two buttons, one for down and one for up?
So when a user presses and holds the down button it appears to scroll down the div by about 10px at a time.
Edit:
The mobile app is actually being compiled with Phonegap, so it won't be a mobile website but an actual application.
The application features dragging and dropping quite heavily and in order to do this using JQuery and HTML, I've had to bind the mousedown, mouseup and mousehover events to touch events.
Because of this the user cannot simply drag the screen to scroll as they would a typical application. Therefore, I have decided to go with physical buttons instead of scrolling the navigation div.
The navigation div is set to have a greater height than the canvas (screen height and width) div. This will be the div the user is scrolling.

Is the div you're talking about scrolling the full page itself? Or is it a specific div that you want to "scroll" within the page (kind of like an iframe)?
Both can be done. If you're scrolling the full page, I'm not sure why you'd want to use buttons rather than let Safari simply handle the standard swipe gestures. But, it could be done this way:
Use fixed positioning on the buttons so that they don't move as the rest of the screen scrolls.
Use use jQuery's .scrollTop method to do the scrolling.
If, on the other hand, you want to make a scroll effect on a single div, without the rest of the page scrolling, then just do the following:
Wrap that div in another div that has overflow:hidden; position:relative
Make the inner div position:absolute
Animate the inner div's top property to create the scrolling effect.

You may find this plugin useful: http://logicbox.net/jquery/simplyscroll/vertical.html
Anyway, why would you need that? The user may be able to scroll normally with a finger swipe if the content is bigger than the screen.

Javascript: don't stop scrolling window if the cursor passes over a scrollable div

I'm building a web app that has a grid of many small scrollable divs (actually, Ace editors), and this grid has enough elements that it is larger than the window. When a user begins scrolling over empty space, I want them to be scrolling the window itself; when a user begins scrolling inside a grid element, I want them to scroll the div contents there. The thing is, if a user begins scrolling over empty space, and then scrolls such that their mouse goes over a grid element, that scrollable div captures all the scrolling events, interrupting the user's flow over the grid and "trapping" them inside the grid element.
I can't manually capture onmousewheel events, since AFAIK there's no way to capture horizontal mouse wheel movement separately from vertical, and I want users on Mac OS X to be able to scroll in all directions. I've thought about using JS to add an invisible div with a very high z-index on the first onscroll event, and removing it as soon as onscroll events aren't triggered for a certain period of time. Haven't yet coded this up, but I'm wondering if there's a better solution, or if there are any potential pitfalls that I haven't thought of. Any help or advice would be great! Thanks!

I think a solution for this would be incredibly difficult due to browser support, and the actual solution, which would probably be something like calculating the scroll, backtracking the div, and applying the scroll to the page.
You could do something like this:
$('div').scroll(function(e){
// figure out how much it has scrolled
window.scrollBy(0,howmuch);
});
I don't recommend this solution in the slightest though, I think the better option would be to set the divs to overflow:hidden; and pick up a solid scroll plugin, and use that to customize the scroll behavior on the divs.

How can I temporarily prevent a scrollable div from scrolling?

Here is my current situation:
I have a web page containing a couple scrollable divs. Each of those divs contains a number of objects. I am using YUI to display popup menus of actions that can be performed on each object. Each object has its own menu associated with it that is constructed and displayed dynamically. The popup menus can be large and can overlap the bounds of the scrollable div.
From what I believe are issues with focus (the menus must be accessible), when I hover the mouse over an action that lies on top of an edge of the scrollable div, the div automatically scrolls, moving the content but leaving the menu stationary. Trying to move the menu dynamically when this happens is not something I want to do as I believe it would provide a poor user experience.
So I need to prevent this focused menu from scrolling the div. My idea for providing the best user interface is to prevent these inner divs from scrolling when a menu is open. This leaves the menu positioned in the optimal location to show the user which item is being acted upon. If the user wants to scroll the box, they can click to close the menu and then scroll normally.
How can I do this? I need a solution that works across the major browsers.
My first thought was to listen to the onscroll event for that particular element. Unfortunately, there does not seem to be an easy way from there to just prevent the scrolling from happening. For one, my JavaScript event code appears to execute after the actual scrolling has occurred.
Then, I thought that since my code is being run after the object has scrolled, I could just reset obj.scrollTop and obj.scrollLeft. Sure enough, this appears to work, though I am worried that on slow browsers the user will see the content inside the div "jump around". Also, it would be really nice if the amount the element scrolls is part of the event object. Is it stuck in there somewhere? I'm looking for an alternative to having to store the scrollTop and scrollLeft variables for this element and then using them while the scrolling is temporarily disabled.
What is the best way to solve this entire problem?

I agree with Anthony regarding the presentation of the functionality you're trying to disallow. If you're going to disable scrolling, then you should make that part of the page visually disabled or removed.
To that end, you can position a semi-transparent div on top of the scrollable div in question, which would capture the mouse events and visually show that the scrollable div is inactive for now. It would be hard to make cross-browser compatible and wouldn't be perfect, but then again very few client-side tricks like this are.

The simple answer is no you can't do this. Its doubly no if you want a cross-browser solution.
Providing the user with the clear affordance that something can be scrolled then denying them that is just plain poor UI design.
Ok so after your edit it turns out you are not actually trying to prevent the user from scrolling.
The main answer remains true though. It sounds as though the focus is going to rectangle (probably an anchor?) that is not fully in view and causes a scroll. Is there a reason this rectangle must get the focus? For accessibility?

What if you didn't have overflow: scroll and instead you used overflow: hidden and provided scroll up/down buttons that allowed the user to scroll when necessary? These buttons could of course be disabled easily.

Though it may not be the answer you are looking for, if you are to set the display value of the div to 'none' while the page loads (from the server) and then have an event wired to the page load (either pageLoad in ajax.net or attach it to the onload event via javascript) that will make the div display set to 'block' .. that would ensure that slower browsers wouldn't see the div 'jumping around' (could even put a 'loading' image in the div to show users it's doing something and not just invisible)
sorry i couldn't provide a more complex/fluent solution.

I found a way to work around this issue. By removing the menu element from the scrollable div and then appending it directly to document.body, the browsers all stop trying to scroll the div to reveal the focused element (even though the element is already completely visible).
Thanks to all for your time and your answers!