Homam's Mind

Monday, January 27, 2014
Sunday, January 12, 2014

D3 Enter - Update - Exit Pattern in LiveScript

Since I first heard of LiveScript a couple of months ago, I've enjoyed programming my small and big JavaScript projects in LiveScript. Here I want to show how LiveScript makes D3 general update pattern easier to work with.



Here's the result showing enter - update - exit pattern in D3 and the gist.

In the above code I'm using LiveScript's property access cascades sugar. Note how it improves the readability of the code and makes it easy to identify enter!, transition! or exit! cascades.

See also how the sampling and shuffle functions are defined by a composition of some functions rather than a for loop that IMHO is much prettier than the original.

Anyway, I enjoy D3 and LiveScript and this two go together like pancakes and syrup!

Tuesday, September 27, 2011

CSSMatrix 3D Transformations

Well I’ve spent a good weekend figuring out CSS3 3D transformations. In short, now I think it is intelligently designed to fit web design needs, however coming from Direct3D background I was looking for a camera in W3C API.

In this post I show how to make a touch sensitive, interactive 3D model of the iPad using matrix transformations.

Although iPad is not a perfect cuboid, for simplicity we assume it is. Google and download pictures of the 6 sides of the iPad. Read this excellent Introduction to CSS 3-D Transforms on how to make 3D cuboids using CSS3. It is fairly easy and straight forward.

[caption id="attachment_255" align="aligncenter" width="122" caption="iPad layers before transformation; six sides stacked on top of each others"]Untransformed layers[/caption]

I want to rotate the model by touching the screen / moving the mouse. We’re not digging into the details of touch event handling here, check out Touching and Gesturing  on the iPhone for a nice discussion on this subject.

Obviously we move our fingers on the phones screen, or the mouse in 2D flat surfaces, but we want to rotate our iPad in 3D space. Luckily any rotation in 3D space can be decomposed to 3 elemental rotations around the axes of a coordinate system (frame of reference), using Euler angles; meaning that a user can rotate the model to a desired state by no more than 3 gestures.

Transformed iPad ModelCheck out the first draft.


It works; you can freely rotate the model in any direction. But something’s not quite right: the UI response to gestures is not intuitive. Sometimes when you move your fingers to the left, the model rotates upward, another time it rotates down-right…. The problem is that every time that you rotate the model you change the orientation of its axes. You can leave your program as it is, it is sellable and in fact I've bought programs with this bug before. The rest of this post explains a solution to this problem.

Linear Transformations


All CSS3 transformations (rotate, scale, skew) are reversible, you can rotate an object 40 degrees clockwise, scale it to 2x bigger, then shrink it to half and rotate it 40 degrees counter clockwise and you end up with the object in its initial state. Another interesting feature of CSS3 transformations is that although an image can be distorted by a transformation, straight lines don’t curve or bend and remain straight under any transformation. Each point of the original image is always mapped to one and only one point of the transformed image. These are the characteristics of linear maps.

Any linear map can be represented by a transformation matrix. In our case, in a 3-dimensional space, it is a 3x3 matrix. I won’t dig into the technical details of matrices, simply because we don’t need to know those details. Check out your old analytic geometry textbook.

Given a transformation matrix M, any point P of our object will be transformed by this matrix product:
P’ = M * P

(Here we use the fact that points can be represented by their position vectors, hence column matrices)

There’s a little thing about translation transformation. In good old geometry, a translation can be represented by a vector (when you translate an object, you move it along a path that has a direction and length), and you find the translated coordinates of a point P by summing up its original coordinates with the translation vector: P’ = P + T.  There’s a trick to combine translation with other forms of linear transformations using 4x4 matrices.

If M is a 4x4 transformation matrix and P is a 4x1 column vector representing the coordinate of a point in space (the last row of the vector is set to 0), then:
P’ = M * P

P’ (the matrix product of M and P) is the coordinate of our point after the object has been transformed by M.

M can represent any state of escalation, rotation, translation, or skewness.

CSSMatrix


CSS gives us the option to define our desired transformation by a 4x4 transformation matrix. This method is virtually useless in CSS declarative way, for a 3D transformation you have to calculate the matrix elements and pass 16 parameters to matrix3d() property function (for an example to see how obscure the code might become, check out rotate3d() definition in W3C’s CSS 3d transforms draft). But it is easy and very convenient to use this matrix in JavaScript code, thanks to DOM’s CSSMatrix interface. Currently (Sep. 2011) WebKit implements this interface by WebKitCSSMatrix type.

We initialize an instance of a WebKitCSSMatrix by passing a correct string value of -webkit-transform CSS property. So one can construct it by something like this:
new WebKitCSSMatrix("scale3d(1,2,1)")
or
new WebKitCSSMatrix("scale3d(1,2,1) rotate3d(0,0,1, 45deg) translate3d(100px, 0, -20px)")

Here’s where this window object’s little useful function comes handy: 'window.getComputedStyle()'. getComputedStyle() takes a DOM Element and returns an instance of CSSStyleDecleration that is a representation of all the style properties currently set for the element. It is also a dictionary. You can get the current transform value by: window.getComputedStyle(element)["-webkit-transform"] or by window.getComputedStyle(element).webkitTransform property. Its value is in form of matrix() or matrix3d(). To get the current CSSMatrix that is applied to an element use:
m = new WebKitCSSMatrix(window.getComputedStyle(element).webkitTransform)

CSSMatrix is indeed a 4x4 matrix (its properties are named m11 to m44), its toString() method returns its CSS representation (in matrix() or matrix3d() form).

It also provides a handful of useful functions for matrix manipulation. These functions don’t mutate the object; they return a new instance of CSSMatrix:

  • multiply

  • inverse

  • translate

  • scale

  • rotate

  • rotateAxisAngle

  • skewX

  • skewY


Check out Apple’s documentation.

I learnt it in a hard way that multiply() function doesn’t exactly work as I understand from the documentations. The text says, and I naturally expected that, given matrices A and B, A.multipy(B) must be equal to A * B in math notation. But it turned out that it is actually equal to B * A.

Back to our original problem, let’s differentiate between the model's frame of reference and the world (device viewport) frame of reference. Your view port (computer’s screen) has a static frame of reference (for our purpose). Viewport axes: Up (Y), Right (X) and Facing you (Z) are attached to the device; they don’t change with respect to the device. But the directions of your 3D model’s axes (X’,Y’,Z’) change as you rotate it inside the viewport. Our UI inconsistent response problem happened because when we move our fingers upward on the device, we expect the model to rotate around device X axis, but rotate3d(1,0,0,#deg) actually rotates the model around its own X’ axis.

Viewport vs Model frame of reference


Luckily rotate3d(z,y,z,#deg) function can rotate the model around any arbitrary axis (defined by vector [x,y,z] here). So the problem boils down to finding, which axis of the rotated object is parallel to the device X and Y axes, after an arbitrary rotation.

We know that rotation can be represented by a linear transformation matrix. If V’ is an arbitrary axis on the model, that was parallel to V (an axis in device frame of reference) prior to the rotation, then we can find what axis on object is now parallel to V after the rotation, by:
V’’ = M * V’

(where M is the transformation matrix that defines the rotation)

If the model is not transformed (when window.getComputedStyle(element).webkitTransform is the identity matrix) V’’ is parallel to V’ parallel to V.

Note that we represent an axis by a vector parallel to it, so the column vector:  represents X axis, [0,1,0] represents Y and [0,0,1] represent Z. A rotation linear transformation can be represented by a 3x3 matrix
M =Transformation matrix (M)

There you go. You can extract CSSMatrix m11..m33 elements and write a little bit of JavaScript to produce V’’. Or use CSSMatrix.multiply() function that takes a CSSMatrix as its argument; then you have to construct a 4x4 representation of axes by just padding the column vector and setting all the other elements to 0.

In JavaScript:
var deviceXAxis = new WebKitCSSMatrix("matrix3d(1,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0)");
var deviceYAxis = new WebKitCSSMatrix("matrix3d(0,0,0,0, 1,0,0,0, 0,0,0,0, 0,0,0,0)");

The result of deviceXAxis.multiply(transformation) is the object’s X’’ axis that is currently parallel to device X axis.

The following function rotates the model around device X and Y axes (resulting in a natural user experience):
function rotateModel (xRot, yRot) {
    // get the current transformation matrix:
var m = new WebKitCSSMatrix(window.getComputedStyle(cube).webkitTransform);
    // Model Y’ axis that is now parallel to device Y axis:
var yAxis = ipad.deviceYAxis.multiply(m);
    // Rotate around Y’:
var m1 = m.rotateAxisAngle(yAxis.m11, yAxis.m21, yAxis.m31, yRot);
    // Model X’ axis that is now parallel to device X axis:
var xAxis = ipad.deviceXAxis.multiply(m1);
    // Rotate around X’:
var m2 = m1.rotateAxisAngle(xAxis.m11, xAxis.m21, xAxis.m31, xRot);
    // Apply the final rotation matrix to the model:
cube.style.webkitTransform = m2.toString();
}

Check out the final product here.
Sunday, July 10, 2011

HTML5 mobile games

For everybody who got here looking for selling their games to my company, you can catch me in twitter @homam, GoogleWindows Live (whichever you like :)).
Thursday, March 11, 2010

Mutually Dependent Systems

In this post I am discussing a problem that I have faced several times in the past year. Simplicity is always a goal in design as it saves resources during development and maintenance. But it's not always clear which design is simpler. Sometimes a seemingly complex design turns out to be simpler to develop, maintain and extend.

In a master-slave architecture, assume S1 is the master. It produces one or more tasks form a given job and transfers them to S2 (the slave); S2 does the tasks and return the results back to S1. S2, the slave, depends on S1, the master.


If the next time that S1 assigns a task to S2 it uses the information that exists in the result of a previous task that had been assigned to S2 then S1 also depends on S2 and we have a mutually dependent couple.

In our terminology the systems are mutually dependent if and only if S1 uses the information it gained as a result of a previous task that it had already assigned to S2. It doesn’t matter if S2 has completed the previous task or not, but it should have reported something to S1 that is useful for S1 for a next assignment of a task to S2.

If S1 is only using the fact that S2 is busy or free then we don't call it a mutual dependency. S1 must use the information that is generated by processing a task at S2. For example a MapReduce system is not a mutually dependent system.

Why is it important? You should have already guessed that S2 is the name of a class of slave systems that work with S1. There could be many instances of S2. Let's define a homogenous mutually dependent system as a system that in which all slaves of S1 are in the same class.

Two slaves are of the same class if they share a common interface for communicating with S1.

Now assume that S3 is also a slave for S1. S3 is in a different class other than S2 if either its input or its output interface is different from S2's.

When designing mutual dependent systems we have to always decide whether to keep the mutual dependencies or to break them by introducing new nodes. It's mainly a decision over complexity. The other factor that may affect your decision is the swiftness of the system. Introducing a new node will usually reduce the responsiveness.

[caption id="attachment_239" align="aligncenter" width="292" caption="Breaking the mutual dependency by using S4 node. Note that S3 is another class and uses a different interface to communicate with S4."][/caption]

For instance a new node must not be added if S1 waits for S2 to return. Generally you should try to keep the number of nodes as small as possible if the operations are not asynchronous.

Homogenous mutual dependency is OK (when the systems are simple and synchronous) but things get much dirtier as we introduce new classes to the system. On the other hand if extensibility is a goal you should try to avoid mutual dependencies.

For a conclusion, use mutual dependent systems in live systems, when a rapid response is required, and try to avoid them by introducing middle nodes if you have many classes of slaves or if extensibility is a goal.
Thursday, February 18, 2010

Canvas Intellisense in Visual Studio

I was playing with HTML5 Canvas element to see how it could be useful in future web based game developments. I like that it is easier than GDI. I haven't yet done much performance testing but it is definitely faster than making games by animating DOM elements.

Recently I had some free time so I decided to create vsdoc documention for Canvas element interface for Visual Studio. I added intellisense (auto competition) and some helps and tips.

Download canvas-vsdoc.js and canvas-utils.js from CodePlex.



It is tuned to work with VS2010, but we can make it work with VS2008 too.

canvas-vsdoc.js contains the intellisense documentation.

canvas-utils.js has a few utility functions (like detecting if the browser supports Canvas) and some enumeration types for things like Line Joins, Repeations, Text Aligns, etc.

To use the intellisense you need to reference canvas-vsdoc.js in the beginning of your JavaScript file, like this:

/// <reference path="canvas-vsdoc.js" />

Note you can just drop the .js file and Visual Studio will write the reference.

Then use a utility method to get a reference to canvas element:
var canvas = Canvas.vsGet(document.getElementById("canvas1"));

Canvas.vsGet(element) receives a HTML element and returns the given element itself if it is in runtime. But in design time it returns Canvas.vsDoc.VSDocCanvasElement object that contains the documentations.

Then you can use the canvas element as usual:
var ctx = canvas.getContext("2d");
ctx.arc(50, 50, 25, 0, Math.PI, true);

Please note canvas-vsdoc.js must not be included  in runtime but canvas-utils.js should be included (if you want to use Canvas.vsGet() and other utilities).

In VS2008 you should trick the environment by assigning the variable that refers the 2D context to Canvas.vsDoc.Canvas2dContext, by something like this:
var ctx = canvas.getContext("2d");
if (typeof DESIGN_TIME != "undefined" && DESIGN_TIME)
ctx = Canvas.vsDoc.Canvas2dContext;

DESIGN_TIME global variable is defined inside canvas-vsdoc.js. In runtime it should be undefined or false.

Just a note: if you still want to work in IE, you will find this Google extension very interesting: http://code.google.com/chrome/chromeframe/

Update: Visual Studio 11 natively supports canvas intellisense.

 

 

 

 

 

 
Wednesday, February 10, 2010

iframe Cookies in Safari

Older Hyzonia games depend on session and authentication cookies. This dependency has been fixed in the newer games by storing session ID in JavaScript variables. The cookie independent services explicitly require a session ID to be sent by their clients.

In this post I am not going to dig into the details of session management in Hyzonia platform, I just want to highlight a series of problems in the old schema that led us to redesign the session management behavior.

Hyzonia games can be embedded in publishers websites using a piece of code we call Hyzobox. Hyzobox basically renders an iframe in the webpage. The internet domain where the actual game is hosted could be different from the publisher's domain. If you have ever tried this before you know that we gonna have a lot of cross site security issues.

To address cross site scripting issues we developed Hyzobox In/Out API. A publisher can control certain things in the game and be notified about the events that are occurring inside the game using In/Out. It is a JavaScript based solution and strangely is widely supported in all major browsers. The In/Out API is not made public yet, but we are using it extensively in www.hyzogames.com. For instance whenever you win in a game Hyzogames.com will be notified about this event (winning) and may show you a message box.

But cookies are another issue. Different browsers have way different behaviors when it comes to handling cookies in iframes.  For starters for it  to works in IE you need a P3P header like this:

CP="IDC DSP COR ADM DEVi TAIi PSA PSD IVAi IVDi CONi HIS OUR IND CNT"

There's a lot to say here, I have a long standing view that P3P is generally useful but this kind of usage is pointless. Anyway for now just add it in your response and relax.

But still Safari rejects the cookies that iframes try to write. The rationale here is that Safari only wants to write cookies from websites that the user directly visits. It's not a bad idea for privacy. Let's assume that you are visiting a fan website for The Grudge! thegrudgefans.com is using  Google AdSense  (put any evil multibillion dollar internet ad service instead of Google :D) to display you some ads or even just in the background. The AdSense is running inside an iframe and it writes a cookie on your computer indicating you're a fan of nonsense horror teen movies. Now it is written on your face that you're a fan of The Grudge. AdSense can use this cookie anywhere else in the internet. OK you got the idea.

The problem was this privacy feature in Safari was causing our Hyzobox User Integration (a kind of Single Sign On service) to break. Safari users can always turn on a checkbox in the preferences to accept all cookies. But it's not the case by default. The workaround is that the page that writes the cookies must be initiated as a result of a direct user request. Literally meaning that prior to writing any cookie you have to provide a hyperlink (an explicit anchor tag) in your iframe that takes the user to the page that writes the cookie.