Triangle Barycentric Interpolation Calculator
Find a point’s triangle weights, interpolate a scalar vertex value and identify outside-triangle extrapolation.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Solve the affine coordinate relation with weights summing to one. Multiply each vertex scalar by its corresponding weight.
P=wA A+wB B+wC C; wA+wB+wC=1; value=wA vA+wB vB+wC vC
Worked example
Vertices (0,0), (2,0), (0,2), values 0,10,20, and P=(0.5,0.5) give weights (0.5,0.25,0.25) and interpolated value 7.5.
Assumptions and input details
A non-collinear 2D triangle and one scalar at each vertex; input magnitudes up to 1e9. A normalized determinant below 1e−12 is rejected. Inside/on classification allows a 1e−12 weight tolerance. A point outside the triangle has a negative weight and the value becomes affine extrapolation, explicitly labelled. This interpolates one scalar linearly; it does not apply perspective correction, clamp to the triangle or infer a physical field.
References: Wolfram Research: barycentric coordinates
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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