Metaballs are, in computer graphics, organic-looking n-dimensional objects. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s.
Each metaball is defined as a function in n-dimensions (i.e. for three dimensions, ; three-dimensional metaballs tend to be most common, with two-dimensional implementations popular as well). A thresholding value is also chosen, to define a solid volume. Then,
represents whether the volume enclosed by the surface defined by metaballs is filled at
or not.
A typical function chosen for metaballs is , where
is the center of the metaball. However, due to the divide, it is computationally expensive. For this reason, approximate polynomial functions are typically used.
When seeking a more efficient falloff function, several qualities are desired:
You were the light in the darkness
That I lived in full of redemption and sin
Even though I was surrounded by the best of friends
My future was looking dim
You gave me hope in a time when I lost control
About to lose my soul
You picked me up from the gutters that I once roamed
Helped my see what I now know
When I thought there was no one there for me
Your light shined on me
You gave me hope, you gave me all I need
You set me free
When I fought against myself, to be as good as I can be
You gave me strength, you gave me what I need
You're everything to me
In the darkest of days you came into my life
It was full of so much strife
Self-destruction was the name of the game that I played
You reinforced the values that I had lost at no price or cost
And even when I slipped into the darkness again
You fought to bring me back in
I hope you know what you mean to me
You mean everything, everything
I hope you know that I'd do anything for you
I mean anything
You made a man out of me when I thought I knew it all
I knew nothing
You brought me hope in my darkest days
I love you more than anything
When I thought there was no one there for me
Your light shined on me
You gave me hope, you gave me all I need
You set me free
When I fought against myself to be as good as I could be
You gave me strength you gave me what I need