Latest Comments

§ narasingM   said on :

good work on the detail. But lacks a complete working example for someone to fully comprehend without referring to other material. Hope you can add.

§ Paulo said on :


Very nice article. Thanks.

§ Paul Watt®   said on :

I apologize about the link.
I will edit this post to point to the latest stuff found on GitHub.


§ Tim said on :

Love the blog, found this entry most interesting. One of the things that drives me nuts is the assumptions about copy rights; to wit; on youtube is a copy of Robert Johnson’s classic “32-20 Blues", its a “tribute” type video with the audio overlaid with some deep south pictures and so on. The guy who put the video together mentions something about a copy right (I forget the attribution) even though the song passed into the public domain years ago. One should never make assertions about things they know NOTHING ABOUT!


§ Ameya V Singh said on :

The download link is broken.
From where can I download the sources mentioned in this article.


§ Paul Watt®   said on :

Thanks for the clarification. I’ll modify my text.

§ serkan said on :


Thank you for the article.

In the “Does it have a name?” part, lvalue expressions that doesn’t have name were described as follows;

“Examples of lvalue expressions that do not have names are string literals and function call expressions that return an rvalue reference.”

Function call expressions that return a rvalue reference are xvalue, lvalue expressions must be function call expressions that return an lvalue, not rvalue.

§ Alien426 said on :

No, it is not fixed.

It used to be a copy of the binary conversion with just the radix changed from 2 to 16.

Now you it reads:
237 / 16 224 D16 (13) (160)
224 / 16 13 E16 (14) (161)

You just put in the numbers from your (hex to dec) comment.

§ Paul Watt®   said on :

Thanks for clarifying, I understand what you were indicating.
It’s now corrected.

Thank you again.

§ Alien426 said on :

The result is correct. The calculation is not. Please fix it.

§ Paul Watt®   said on :

Thanks for double-checking my work.

However, 0xED is the correct conversion for 237 from decimal to hexadecimal. A quick way to verify this is to convert 0xED back to decimal:

0xE(14) * 16 + 0xD(13) * 1 = 224 + 13 = 237

The quotient (answer to the division) is the value that we want to fill in the place-value spot during number conversion.
The remainder is what is left and carries over to the next lower place-value column.

§ Paul Watt®   said on :

k_pi_inverse is 1/pi:


§ Alien426 said on :

The conversion of decimal 237 to hexadecimal is incorrect.

It should be:
237 / 16 = 14, remainder 13 -> 0xD
14 / 16 = 0, remainder 14 -> 0xE

§ Mathieu   said on :

What value should k_pi_inverse be?

§ Tianxiao Jiang   said on :

Cross origin compile on coliru seems not working now, neither on nor here. It was working just a few days ago. I was trying to do the same thing with coliru, any idea ?

§ Scott said on :

k_pi and k_pi_inverse not defined

§ Rolandcharcker said on :

That is fascinating post and thank you for sharing. There are things here that I didn’t think some time recently. On account of cool such a position, to the point that is extremely elegantly composed.

§ Paul Watt®   said on :

@Semi Essessi

Thanks for you input.

How do you deal with rotating a model and avoid matrix multiplication?

§ Semi Essessi   said on :

i have some strong opinions about this stuff having worked a lot out for myself from nothing… vectors, matrices and trig are overkill to start with, and introducing them so early obscures the simplicity of what is actually necessary imo…

as an obvious example, generic matrix multiplication is pretty useless (and classically confusing) compared to the change of basis/coordinate system that happens to be the same operation as multiplying square matrices.

§ Troy said on :

This is probably the most thorough explanation I’ve seen on this subject. I found the tables and tips for navigating hexadecimal to be really helpful.

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