Rendering a reflection about an arbitrary plane

Sage

Posts: 1,199
Joined: 2004.10

Post: #1

Dec 19, 2007 — 11:46 AM

So I've rendered reflections ( for water ) in the past, but my reflections were restricted to a plane described as simply a function of Z ( where Z is up ).

My code looked something like so ( taken from my water demo, leaving out clip planes ):

Code:

glPushMatrix();

glTranslatef( 0.0f, 0.0f, _currentWaterLevel );

glScalef( 1.0, 1.0, -1.0 );

glTranslatef( 0.0f, 0.0f, -_currentWaterLevel );

renderScene();

glPopMatrix();

What I'm wondering, is how I can reflect about an arbitrary plane, described in (a,b,c,d) format. I imagine a matrix can be constructed which would represent the inversion, but I'm weak. Any suggestions?

mattz

Member

Posts: 45
Joined: 2006.07

Post: #2

Dec 19, 2007 — 12:02 PM

I'm pretty sure you can use one of these: http://en.wikipedia.org/wiki/Householder_reflection

Let n = (a, b, c) be the normal of the plane and let p be some point the plane passes through. Then make the 3x3 matrix H = I - 2nn^T =

Code:

[ 1-2*a^2,  -2*a*b,  -2*a*c]

[  -2*a*b, 1-2*b^2,  -2*b*c]

[  -2*a*c,  -2*b*c, 1-2*c^2]

Then do something like

Code:

glTranslatef(px, py, pz)

glMultMatrixf(H)

glTranslatef(-px, -py, -pz);

TomorrowPlusX

Sage

Posts: 1,199
Joined: 2004.10

Post: #3

Dec 19, 2007 — 01:51 PM

That looks like what I'm looking for. I'll give it a stab ( unfortunately, I won't be able to for a couple more days, as I work out the render to FBO pipeline in my current codebase ).

Thanks!

TomorrowPlusX

Sage

Posts: 1,199
Joined: 2004.10

Post: #4

Jan 14, 2008 — 07:51 AM

It's been a few weeks, but as of last night reflection rendering in my code is robust, flexible, reasonably fast, and works like a champ. I wanted to post a couple screenshots just to show off.

[Image: reflectiontest-2008-01-14-03.png]

[Image: reflectiontest-2008-01-14-03.png]

[Image: reflectiontest-2008-01-14-02.png]

Thanks for the help! Without the householder transform I'd never have gotten this working!

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