Coding Math: Episode 22 - 3D - Postcards in Space

Finally, we make it into the realm of the third dimension. Or at least half way into the third dimension.

[johnconley]

No need to apologise for the lack of coding...your voice is enough to calm anything and everything : ¬ )

[kevnar]

I used this formula for computing the odds of hitting a guy with an arrow shot in an RPG I made. The target size get smaller with distance. How much smaller? Well, just use Keith's formula.

if z = 0, you have a 100% chance to hit the target. If z = 600, you have a 33% chance to score a hit. And so on. Makes for interesting dice rolls.

[kevnar]

Here's the code for those of you not using canvas translation:

xOffset = width / 2; // sets the vanishing point to center screen
yOffset = height / 2;

perspective = fl / (fl + shapePos.z);

zSize = shapeSize * perspective;
xPos = xOffset + (shapePos.x * perspective) - (zSize / 2);
yPos = yOffset + (shapePos.y * perspective) - (zSize / 2);
G.FillRect(xPos, yPos, zSize, zSize);


shapeSize is the size of the rectangle. Keith set his to 200. You should be able to figure the rest out.

[jimsmart]

In 3d programming, these are often called billboards or billboard sprites.

[khushwantdafre]

I recently started following these tutorials and for me the best thing about these videos are Keith's sense of humour 🤣🤣. Last video was posted on this channel way back in 2017. I hope you are doing well Keith and also thank you for these amazing tutorials, they have helped me a lot.

[sociamix]

Hi, can you explain from where comes the perspective formula please ? Otherwise nice video !

[thawfeekyahya]

Thanks for the explanation Kieth. Love your tutorials.

[lucasmachain]

you impressed me with the exampless that was nice 

[TheGrifdail]

Why do you first translate by x*perspective ans then do the scale ? By doing the scale first, the drawing position will also be scale by perspective, then you just have to draw the object at is original x and y coordinate.

[BlenderGameArtist]

you're tutorials are exactly what I was looking for!!

[joaquimjesus]

thank you so much for all.
do you have a video about raycasting?

[alekmoth]

I dont understand why focal length (the diameter of an eye basically) is a number as large as 300 (large relative to distances u use in the world).

[cygil]

@13:50 You didn't order the blit order of the objects by by z-axis, taking advantage of the painter's algorithm for occlusion? It would take literally a minute to explain.

[joaquimjesus]

why 'fl', on perspective, is 300?

[Revlis]

Are the z-index problems with the last example just because you originally set it up to go away from the camera as opposed to towards?

[cygil]

I find your tutorials a little long winded (perspective -- I get it, get to the formulas already) but others seem to appreciate it so I guess there's a niche for it.

[DasAntiNaziBroetchen]

It's not just how stuff was rendered in Wolfenstein. It's how every single particle effect is rendered in every single game.