• Announcements

    • khawk

      Download the Game Design and Indie Game Marketing Freebook   07/19/17

      GameDev.net and CRC Press have teamed up to bring a free ebook of content curated from top titles published by CRC Press. The freebook, Practices of Game Design & Indie Game Marketing, includes chapters from The Art of Game Design: A Book of Lenses, A Practical Guide to Indie Game Marketing, and An Architectural Approach to Level Design. The GameDev.net FreeBook is relevant to game designers, developers, and those interested in learning more about the challenges in game development. We know game development can be a tough discipline and business, so we picked several chapters from CRC Press titles that we thought would be of interest to you, the GameDev.net audience, in your journey to design, develop, and market your next game. The free ebook is available through CRC Press by clicking here. The Curated Books The Art of Game Design: A Book of Lenses, Second Edition, by Jesse Schell Presents 100+ sets of questions, or different lenses, for viewing a game’s design, encompassing diverse fields such as psychology, architecture, music, film, software engineering, theme park design, mathematics, anthropology, and more. Written by one of the world's top game designers, this book describes the deepest and most fundamental principles of game design, demonstrating how tactics used in board, card, and athletic games also work in video games. It provides practical instruction on creating world-class games that will be played again and again. View it here. A Practical Guide to Indie Game Marketing, by Joel Dreskin Marketing is an essential but too frequently overlooked or minimized component of the release plan for indie games. A Practical Guide to Indie Game Marketing provides you with the tools needed to build visibility and sell your indie games. With special focus on those developers with small budgets and limited staff and resources, this book is packed with tangible recommendations and techniques that you can put to use immediately. As a seasoned professional of the indie game arena, author Joel Dreskin gives you insight into practical, real-world experiences of marketing numerous successful games and also provides stories of the failures. View it here. An Architectural Approach to Level Design This is one of the first books to integrate architectural and spatial design theory with the field of level design. The book presents architectural techniques and theories for level designers to use in their own work. It connects architecture and level design in different ways that address the practical elements of how designers construct space and the experiential elements of how and why humans interact with this space. Throughout the text, readers learn skills for spatial layout, evoking emotion through gamespaces, and creating better levels through architectural theory. View it here. Learn more and download the ebook by clicking here. Did you know? GameDev.net and CRC Press also recently teamed up to bring GDNet+ Members up to a 20% discount on all CRC Press books. Learn more about this and other benefits here.
Sign in to follow this  
Followers 0
knarkowicz

Perspective correct depth interpolation

5 posts in this topic

Hi,

I'm writing a depth only software rasterizer and have a few questions about perspective correct depth interpolation.

Vertex position in homogeneous coordinates in clip space: [x, y, z, w]
Vertex position after projection: [x', y', z'] = [x/w, y/w, z/w]

1. In some articles they say that You should interpolate z/w and 1/w. And later divide it to calculate persp corr depth. Other ones (C. Hecker's texture mapper docs) say that You can just interpolate 1/z'. This two ways lead to two different equations, so what is the correct way?

2. If it's ok to interpolate 1/z', then what to do, when z' is 0? For example DirectX style projection matrix returns z' from [0;1] range. Should I tweak it to have z' in (0;1] range or am I missing something?
0

Share this post


Link to post
Share on other sites
I haven't done the math in a long time, but I don't see why you would want to interpolate 1/z'. 1/w or 1/z is correct I think, it doesn't really matter since w depends linearly of z. You can either interpolate 1/z and do the inverse to get the actual depth, or interpolate z/w and 1/w and divide z/w by 1/w.

So you dont have to worry about z' being equal to 0 (which it will be for a point in the near plane), since you interpolate 1/w, which will never be zero. w will usually be a multiple of your z coordinate, so if it's equal to 0, it will be clipped away by the near plane.

[Edited by - zurekx on September 7, 2010 3:54:03 PM]
0

Share this post


Link to post
Share on other sites
Quote:
Original post by zurekx
Well z' is only gonna be 0 when z is zero. This should never happen since you got a near plane and everything behind it should be clipped away.


By DirectX convention in clip space z has range [0;w] and 0 means a point on the near plane.

Quote:
Original post by zurekx
I haven't done the math in a long time, but I don't see why you would want to interpolate 1/z'. 1/w or 1/z is correct I think, it doesn't really matter since w depends linearly of z. You can either interpolate 1/z and do the inverse to get the actual depth, or interpolate z/w and 1/w and divide z/w by 1/w.


I think I can't just interpolate 1/z, because it's in homogeneous coordinates, so I need to include division by w somewhere.
0

Share this post


Link to post
Share on other sites
I just changed my post a little bit before I saw your answer. I haven't worked with the matrices in DirectX, but usually the z clip coordinate is in [-1, 1]. But you shouldnt divide by the z clip coordinate, you should divide by w.

No you shouldnt use just 1/z, since you are using homogenous coordinates and projection matrices and such things. But if you're just thinking, "hey I wanna draw a triangle", you can get away with interpolating 1/z. But if you're somewhat serious and want to make things thw right way, you use a projection matrix. Then you should interpolate 1/w. This will _basically_ be the same thing since w usually is a multiple of z. Maybe I'm mixing things up a little bit though.

The important things though are: w will be a multiple of z. It will never be 0 since it's a multiple of z, and the minimum value of z is the near-plane, which is never 0. It doesn't really matter if you interpolate 1/z or 1/w, but you should use 1/w if you use homogenous coordinates, that's standard.
0

Share this post


Link to post
Share on other sites
I'll be using this rasterizer for geometry culling, so it needs to be accurate and as fast as possible. That's why I asked if the 1/z' way is correct, as interpolating 1 attribute is much faster than interpolating 2 attributes and multiplication per pixel :). Anyway thanks for answers.
0

Share this post


Link to post
Share on other sites
Actually, I looked on the page you posted on some of the DX matrices, and you can use 1/z' aswell if you'd like. Sorry if I confused you, I've never written a rasterizer properly with homogenous coordinates. Anyway, for a depth buffer you could use 1/z'. But you can use 1/w aswell as you don't need the exact z-values. Since w is a multiple of the z-coordinate before projection, it can be used for depth tests.

Wait again :) Sorry if I change my mind all the time, I've had a few glasses of wine :) But you should be able to interpolate just z', not 1/z'.

Let's work it out. If you have a world space coordinate (x, y, z, 1) and you multiply it with the projection matrix, you should have something on the form (xxx, xxx, z*a + b, z * c), for some constants a,b,c. Now if you divide the new z-coordinate by the w-coordinate (to obtain what you called z'), you should get something like Constant1 + Constant2 / z. This is a number that depends on the inverse of z. You should be able to interpolate it linearly in screen space, and just store that value in the depth buffer for comparision.
1

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now
Sign in to follow this  
Followers 0