• 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
  • entries
    22
  • comments
    30
  • views
    42481

The World

Sign in to follow this  
Followers 0
jwezorek

1645 views

For the game I'm working on I need to have sprites that travel along curving paths.

I'm talking about the sprites traveling along somewhat arbitrary curves, meaning curves that look good, not curves that result from gravity or other physical forces. If you need those kinds of curves, e.g. the parabolic trajectories of cannonballs, you need to simulate the forces acting on the sprites and that is not what I'm talking about in this post.

Caveat aside, an arbitrary curving path is a pretty common thing to need but I think is unnecessarily headache-inducing because curves in graphics are just confusing. Maybe you've found yourself thinking

  • I don't know what the difference between a spline, a bezier curve, a bezier curve of various degrees, a B-spline, a t-spline, etc. is.
  • I don't know which of the things mentioned above I need.
  • Every time I try to read the wikipedia article on these things the math gets heavy and my eyes glaze over

    etc.?

    So assuming it's not just me, as a public service I'm going to try to clear this up.

    Short version, if you need to have a sprite that travels along a curving path from point A to point B in x amount of time, you probably need a cubic bezier curve and generally, in 2d game programming, all you will ever need probably is n cubic bezier curves possibly concatenated together. You can concatenate them yourself if you need to do that, so what you need is a way to define a cubic bezier and a function to get the point along the bezier at some time t. Despite what you would think from trying to read the literature, this turns out to be trivial -- I mean less than a dozen lines of code.

    More thoroughly, explaining away my bulleted list above:

    • A spline is a more general term than a "bezier curve": a bezier curve is a particular polynomial function (that I will implement below) that defines a curve that goes from point A to point B given some control points. A bezier spline is an aggregation of n of these. A general spline can be an aggregation of other kinds of curves e.g. a B-spline is composed of a bunch of curves that are generalizations of bezier curves.
    • The only kinds of beziers you need to be concerned with are quadratic and cubic beziers. Quadratic beziers are just parabolas and are not interesting. Cubic beziers are curves that go from point A to point B and are tangent to a given line at A and tangent to given line at B. They are defined by A and B plus two other control points that define the tangent lines and the weight that the tangent lines have on the curve.
    • Cubic bezier curves are easy to implement. See below.

      So here is my curve "library"

      Bezier.h#include class Bezier { private: float x1_, y1_, x2_, y2_, x3_, y3_, x4_, y4_; public: Bezier(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4); std::pair getPoint(float t) const;};

      Bezier.cpp

      #include "Bezier.h"Bezier::Bezier(float x1, float y1, float x2, float y2, float x3, float y3, float x4, float y4) : x1_(x1), y1_(y1), x2_(x2), y2_(y2), x3_(x3), y3_(y3), x4_(x4), y4_(y4) {}std::pair Bezier::getPoint(float t) const { float x = (x1_+t*(-x1_*3+t*(3*x1_ - x1_*t))) + t*(3*x2_+t*(-6*x2_ + x2_*3*t)) + t*t*(x3_*3-x3_*3*t) + x4_*t*t*t; float y = (y1_+t*(-y1_*3+t*(3*y1_ - y1_*t))) + t*(3*y2_+t*(-6*y2_ + y2_*3*t)) + t*t*(y3_*3-y3_*3*t) + y4_*t*t*t; return std::pair(x,y);}

      You define a cubic bezier by making a Bezier object giving the constructor four points. (x1,y1) and (x4,y4) will be the start and end of the curve. The curve will be tangent to line segment (x1,y1)-(x2,y2) at its start and tangent to (x3,y3)-(x4,y4) at the end. To get a point along the curve call getPoint(t) where t=0.0 gives you (x1,y1), t=1.0 gives you (x4,y4), and 0.0 < t < 1.0 gives you the point along the curve in which 100t percent of the curve has been traversed e.g. 0.5 is halfway (in terms of t not arc-length unfortunately).

      So that's it. Code is here. I also included a Win32 GDI project that draws cubic beziers, screenshot below. (The sample program is also a little example of how to write a very basic Win32 program, which these days younger programmers seem to appreciate as a sort of parlor trick...)
      bezier_screenshot.png

      Source

6
Sign in to follow this  
Followers 0


2 Comments


Looks nice :)

 

A consideration: wouldn't it make more sense as a stand-alone function rather than a class? For that matter, a header file with a single inlined function (perhaps one for each type of curve you support) might make the most sense. Just a thought~!

0

Share this comment


Link to comment

You could do it either way. This way suits my purposes because the curves are going to be paths that sprites travel along and as such are part of the game state that needs to be maintained across iterations of the game loop. On the other hand, if I was just drawing curves, then, yes, a free function would make more sense.

0

Share this comment


Link to comment

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