Perspective Transform Calculator
Fit a planar homography to four source/destination point pairs and map a query coordinate with reconstruction residuals.
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
Normalize the point sets, solve eight projective coefficients and apply the resulting 3 by 3 homogeneous coordinate matrix.
u=(h11x+h12y+h13)/(h31x+h32y+1); v=(h21x+h22y+h23)/(h31x+h32y+1)
Worked example
Mapping the unit square to a square twice as wide and tall sends query (0.5,0.5) to (1,1). All four fitted correspondences reconstruct with zero error apart from floating-point rounding.
Assumptions and input details
Exactly four correspondences with no three collinear in either plane. Coordinates can be pixels or another consistent planar system. Degenerate fits and points near a projective horizon are rejected; transforms with unsupported bottom-right normalization are rejected. No image is uploaded or edited. Lens distortion, noisy calibration and nonplanar scene depth are excluded.
References: OpenCV: planar homography and homogeneous 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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