then you should be reminded about how horrible you are.
I'm not ignorant. That's my opinion, and your worthless trolling is your horrible opinion.
I love her legacy!
Me too! Deep Throat was a classic! The way she... uh... wait -- Ada? Ada Lovelace? Uh, I mean, wow, yeah, math... and stuff.
Sigh. Typos in the rotation. Should have been:
Rotation: X = X * cos(theta) - Y * sin(theta); Y = Y * cos(theta) + X * sin(theta);
No. I am one of the primary authors of what might be fairly described as a Photoshop-class application -- one with far more layer modes and built-in filters than Photoshop, as well as a full-bore built-in ray tracer and texturing facility. It is also considerably smaller and faster than Photoshop in the identical system environment. I am also the author of multiple realtime video and arcade games, etc. I'm telling you flat out that matrices are not required. Period.
Matrices may be the only way you know how to do these kinds of graphics; but they definitely aren't the only way to do it.
Just to take your example: "if you have 3-vectors (i.e. points relative to the origin in 3-space), any global linear transformation is represented by a matrix multiplying each vectors"
The correct way to state this is: "if you have 3-vectors (i.e. points relative to the origin in 3-space), any global linear transformation can be represented by a matrix multiplying each vectors." Here is the non-matrix approach (and of course, there's always polar, which can also be easily handled.) This is for 2D points; 2D vectors and 3D points and vectors are all just a further (and trivial) generalizations of the following:
Translation: X += deltaX; Y += DeltaY
Rotation: X = X * cos(theta) - Y * sin(theta); Y = Y * cos(theta) + Y * sin(theta);
Scaling: X *= Xfactor; Y *= Yfactor
Shadows and reflections can be trivially accomplished with more of the same. Basically: R = 2(V dot N)N - V
"dot" is just the dot product, which again is a trivial combination of the lowest math primitives.
You are confusing the fact that matrices can be used to do something with the idea that matrices are the something.
With algebra, trig, and basic math in hand, the programmer's doors to 2D and 3D graphics are wide open.
The government doesn't obey the law.
Your phone is always awake, or can be, which is to say, the CPU running, albeit in a lower power state. From there, it takes very little energy to simply record what the mic is picking up. It doesn't need to be translated, and it can be sent, compressed, at widely spaced intervals in terms of battery load. It could be sent while you are otherwise connected. You'd be unlikely to notice a difference in power consumption.
Funny. Also precisely on target.
When speech recognition gets "decent", as TFS inaccurately states, which is to say, when it's good enough to understand me as well as a human does, then a lot of things will change. For instance, I wouldn't be typing this on a keyboard. I'd be speaking, which is quite a bit faster than typing. Probably never touch my phone other than to slip it into a pocket. Especially after there's a decent, power-efficient wearable display, or an in-eye projection, in front of face hologram, etc.
Right now, what the author calls "decent", I would describe as not even close to acceptable, with a grace note of "better than nothing."
I think it'll be a white yet, based on the crappy stuff available right now.
On the other hand, speech synthesis is actually decent at this point in time.
panic: kernel trap (ignored)