• 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
DmitryNik

Math question

3 posts in this topic

Hello.

Recently I found an interesting assignment. I did it almost 2 years ago and some how I figured out how to do it then. But not now. Could anybody, please, explain me, why this particular problem was solved with a help of the dot product? See problem below.

We have a line l=[0, 1, 2] + a*[-3, 4, 7], which is perpendicular to the plane W. Also plane W contains the point Q=[3, 5, -3]. We have to find the equation of the plane W.

The solution was: const = dot_product([-3, 4, 7], [3,5,-3]) => W's equation is -3x + 4y + 7z = const.

Problem is, I can't remember, what I was thinking of back to those days. I need to understand this solution for solving one problem in the game.
I'll repeat the question here once again:

Could anybody, please, explain me, why this particular problem was solved with a help of the dot product?

Thank you in advance.
0

Share this post


Link to post
Share on other sites
If -3x + 4y + 7z = const is the equation for the plane, then this equation must be true for every point on the plane. Q is a point on the plane so -3*3 + 4*5 + 7*-3 = const must be true. -3*3 + 4*5 + 7*-3 is the same as (-3, 4, 7)·(3, 5, -3).
1

Share this post


Link to post
Share on other sites
[quote name='SiCrane' timestamp='1352040388' post='4997185']
If -3x + 4y + 7z = const is the equation for the plane, then this equation must be true for every point on the plane. Q is a point on the plane so -3*3 + 4*5 + 7*-3 = const must be true. -3*3 + 4*5 + 7*-3 is the same as (-3, 4, 7)·(3, 5, -3).
[/quote]

Thank you. You helped me. I guess, I have to read my old notes through more carefully =)
0

Share this post


Link to post
Share on other sites
A normal vector is perpendicular to all vectors in a plane. Now let [eqn]\left(x, y, z\right)[/eqn] be a point on the plane. We can now form a vector on the plane with [eqn]\left(x, y, z\right) - \left(3, 5, -3\right)[/eqn]. For this vector to be perpendicular to the normal vector (given by the line), their dot product must equal 0. So we have:
[eqn]
\left(-3, 4, 7\right) \cdot \left(\left(x, y, z\right) - \left(3, 5, -3\right)\right) = 0
[/eqn]
Distributing the dot product yields
[eqn]
\left(-3, 4, 7\right) \cdot \left(x, y, z\right) = \left(-3, 4, 7\right) \cdot \left(3, 5, -3\right)
[/eqn]
And expanding yields
[eqn]
-3x + 4y + 3z = -10
[/eqn]
0

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