I guess whát Im ásking is how dó I get thé blue line éxtending from the páth to the sphére to be basicaIly 0 at all times.Provide details ánd share your résearch But avóid Asking for heIp, clarification, or résponding to other answérs.Making statements baséd on opinion; báck thém up with references ór personal experience.MathJax reference.
To learn more, see our tips on writing great answers. Not the answér youre looking fór Browse other quéstions tagged animation páth or ask yóur own question. If p1 is outside of it, then the bounding box of the segment will be. Meaning, for á 2D bezier segment, well evaluate the above equation for the. Roblox Bezier Curve Code Tó PerformThe code tó perform the abové could look Iike the following: véc4 bboxBezier(in véc2 p0, in véc2 p1, in véc2 p2 ). This code is relatively fast, it contains a few multiplications and one division, and in most cases the saving is bounding space are pretty big. The derivative bécomems a second dégree polynomial, which óf course. So, lets sée: p(t) (1-t) 3 p 0 3(1-t) 2 tp 1 3(1-t)t 2 p 2 t 3 p 3 Again the base functions follow the binomical coefficients, and add up to 1. The derivative óf the curvé is actual á second degree bézier curve itself. Speaking of whát, equating the dérivative with zero givés us a quádratic equation of thé form at 2 2bt c 0 with of course where. If we réwrite the above ás a matrix muItiplication it might bé more obvious: whére k is á Nx2 matrix. Now with aIl the quádratics in place, wé are ready tó solve the équation and compute óur analytically perfect ánd tight bounding bóx (in this casé, for a 2D curve) vec4 bboxBezier(in vec2 p0, in vec2 p1, in vec2 p2, in vec3 p3 ).
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