Description
Construct a counterclockwise mathematical-plane rotation from explicit radians, no screen-y convention inferred.
A planar affine transform combines a linear map and translation. This family stores [a,b,c,d,e,f], mapping [x,y] to [a×x+c×y+e,b×x+d×y+f]. Positions include translation; displacements use only the linear block, and normal covectors use its inverse transpose. Composition order changes the result.
Construct a counterclockwise mathematical-plane rotation from explicit radians, no screen-y convention inferred.
When to use this tool
Use this tool to construct a counterclockwise mathematical-plane rotation from explicit radians, no screen-y convention inferred.
How to use the tool and how it works
- Enter radians using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.matrix. Interpret signs, units, ordering and null values using the rules below.
Return [cos(radians),sin(radians),−sin(radians),cos(radians),0,0]. This rotates counterclockwise in the usual Cartesian plane with upward-positive y.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radians | Rotation angle in radians, counterclockwise in an upward-positive y plane. | Finite number satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.matrix | Resulting six coefficients [a,b,c,d,e,f] under the stated map and composition order. |
{
"input": {
"radians": 0
},
"output": {
"result": {
"matrix": [
1,
0,
0,
1,
0,
0
]
}
}
}Limitations and assumptions
- The angle is in radians. A downward-positive screen y axis changes visual rotation direction; no screen convention is inferred.
- Matrices have six finite coefficients. Point/vector inputs have two components within ±1,000,000,000; rectangle bounds are likewise bounded and ordered. Coordinate units and axis directions are caller-defined. No conditioning threshold is inferred for inversion.
- Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Check coefficient layout and application order when exchanging matrices. Use point, displacement or normal operations according to the quantity being transformed, and a separate conditioning analysis for numerically sensitive inverses.
References
Similar or alternative tools
- Affine Matrix About Anchor Transform
Move the linear transform’s origin to an explicit anchor, preserving existing translation.
- Affine Axis Basis Image
Expose origin image and linear basis-vector images separately, avoiding translation contamination of displacement axes.