CODEWITHSUNDEEP
c++opengl3d2dbezier
RRIL97
RRIL97

Reputation: 868

Bezier Curves OpenGL Move 3d Space According to 2d space

I am trying to think about the following problem logically:

Move an object in the 3d space in a fashion that represents a 2d user-generated bezier curve.

As of right now, the user can create his own bezier curve (Which can be seen on the right - I render it via a shader and have access to the x,y of each control point) . As of right now it has 4 control points that are moveable.

enter image description here

I can't seem to think of a way to convert this 2d curve into 3d space movement. Trying to achieve the following:

enter image description here

From a lot of googling, I did find some resources but they all had info about how to convert the 2d point into 3d space and that is not what I want.

Thanks to whoever tries to help, currently lost. I don't need code but more of actual help in approaching such a problem.

Great day.

Upvotes: 0

Views: 479

Answers (1)

Botje
Botje

Reputation: 30807

In a two-dimensional plane, a point is defined by one or more combinations of its two basis vectors. (More combinations are possible if the two basis vectors are not orthogonal)

To project a point onto a three-dimensional plane, you need to embed the two-dimensional vectors b1 and b2 into three-dimensional space and apply a translation t (if needed). In general, this matrix looks like:

[ b1x b2x tx ]
[ b1y b2y ty ]
[ b1z b2z tz ]

and you multiply (x,y,1) by the matrix above. If you multiply by (x,y,0) the translation is ignored which is not what you want in general.

Luckily, if you stick to an axis-aligned plane this is a lot simpler. If we pick the z=0 plane, then the basis vectors are (1,0,0) and (0,1,0) and the translation is (0,0,0). The matrix then becomes

[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 0 ]

and (x,y,1) times that matrix is just (x,y,0).
In other words, you can simply do:

vec2 bezier_2d = bezier(t);
vec3 bezier_3d = vec3(bezier_2d.x, bezier_2d.y, 0);
vec3 box_pos = original_pos + bezier_3d * scale;

where bezier(t) computes the value of the bezier function for a given timestep.

Upvotes: 1

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