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THE FEUTEX TOOLKIT

Quadratic Bézier Point and Tangent

Evaluate a point and tangent on a quadratic Bézier curve from three control points.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaX = (1-t)**2*x0+2*(1-t)*t*x1+t**2*x2; Y = (1-t)**2*y0+2*(1-t)*t*y1+t**2*y2; Dx = 2*(1-t)*(x1-x0)+2*t*(x2-x1); Dy = 2*(1-t)*(y1-y0)+2*t*(y2-y1)
Sources and model references

Worked example

Inputs

X0
0 number
Y0
0 number
X1
2 number
Y1
4 number
X2
4 number
Y2
0 number
Curve parameter
0.5 fraction

Expected results

X
2 number
Y
2 number
Dx
4 number
Dy
0 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "x0": 0,
  "y0": 0,
  "x1": 2,
  "y1": 4,
  "x2": 4,
  "y2": 0,
  "t": 0.5
}

Accuracy and scope

Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.