See hou.Geometry.transformPrims() and hou.Matrix4.explode() for matrix transform examples.

## Functions

```
buildTranslate(tx, ty, tz)
```

→ hou.Matrix4

Returns a transformation matrix containing only a translation. You can build more complex transformations by multiplying this with another transform matrix.

You can supply three float values for x, y, and z, or a sequence of three floats, or a hou.Vector3.

forward_z = hou.hmath.buildTranslate(0, 0, 1) forward_x = hou.hmath.buildTranslate(hou.Vector3(1, 0, 0))

```
buildRotateAboutAxis(axis, angle_in_deg)
```

→ hou.Matrix4

Returns a transformation matrix containing only a rotation computed from an axis and a rotation amount. You can build more complex transformations by multiplying this with another transform matrix.

`axis`

A hou.Vector3 normal defining an axis to rotate around. For example, `hou.Vector3(0, 1, 1)`

would rotate around a diagonal pointed along positive Y and Z.

`angle_in_deg`

Number of degrees of rotation around the axis to store in the matrix.

```
turn_45_around_yz = hou.hmath.buildRotateAboutAxis(hou.Vector3(0, 1, 1), 45)
```

If you want to convert Euler angles into a corresponding axis and angle, you can use the following code:

def extractAxisAndAngleFromRotateMatrix(m): ''' Given a matrix, return an (Vector3, float) tuple containing the axis and angle. See Wikipedia's rotation representation page for more details. ''' import math acos_input = (m.at(0, 0) + m.at(1, 1) + m.at(2, 2) - 1.0) * 0.5 if acos_input < -1.0 or acos_input > 1.0: return None angle = math.acos(acos_input) if angle >= -1e-6 and angle <= 1e-6: # There is no rotation. Choose an arbitrary axis and a rotation of 0. return hou.Vector3(1, 0, 0), 0.0 inv_sin = 1.0 / (2.0 * math.sin(angle)) axis = hou.Vector3( (m.at(1, 2) - m.at(2, 1)) * inv_sin, (m.at(2, 0) - m.at(0, 2)) * inv_sin, (m.at(0, 1) - m.at(1, 0)) * inv_sin) return axis, hou.hmath.radToDeg(angle) def eulerToAxisAndAngle(angles): return extractAxisAndAngleFromRotateMatrix(hou.hmath.buildRotate(angles))

See Wikipedia’s axis angle page and rotation representation page for more information.

```
buildRotateZToAxis(axis)
```

→ hou.Matrix4

Returns a transformation matrix rotating the z-axis onto the given axis. You can build more complex transformations by multiplying this with another transform matrix.

`axis`

A hou.Vector3 defining an axis to rotate the z-axis to.

```
rotate_z_to_x = hou.hmath.buildRotateZToAxis(hou.Vector3(1, 0, 0))
```

The rotation picked is the shortest rotation. If the goal vector is pointed the opposite direction of the z-axis, an arbitrary but consistent rotation that maps to the negative z-axis will be picked.

```
buildRotate(rx, ry, rz, order="xyz")
```

→ hou.Matrix4

Returns a transformation matrix containing only a rotation, given Euler angles in degrees. You can build more complex transformations by multiplying this with another transform matrix.

You can supply three float values for x, y, and z, or a sequence of three floats, or a hou.Vector3.

xform1 = hou.hmath.buildRotate(45, 45, 0) xform2 = hou.hmath.buildRotate(hou.Vector3(90, 0, 90))

`order`

A string containing a permutation of the letters `x`

, `y`

, and `z`

that controls the order of rotations.

See Wikipedia’s Euler angles page for more information.

```
buildScale(sx, sy, sz)
```

→ hou.Matrix4

Returns a transformation matrix containing only a scale. You can build more complex transformations by multiplying this with another transform matrix.

You can supply three float values for x, y, and z, or a sequence of three floats, or a hou.Vector3. To apply a uniform scale, use the same value for x, y, and z.

stretch = hou.hmath.buildScale(2, 1, 1) uniform = hou.hmath.buildScale(hou.Vector3(2, 2, 2))

See hou.Geometry.createNURBSSurface() for an example.

```
buildShear(shearx, sheary, shearz)
```

→ hou.Matrix4

Returns a transformation matrix containing only a shear. You can build more complex transformations by multiplying this with another transform matrix.

You can supply three float values for x, y, and z, or a sequence of three floats, or a hou.Vector3.

See Wikipedia’s shear matrix page for more information.

```
buildTransform(values_dict, transform_order="srt", rotate_order="xyz")
```

→ hou.Matrix4

Takes a dictionary containing mapping strings to vectors (such as produced by hou.Matrix4.explode()), and returns a hou.Matrix4 transformation. You can use this to explode a matrix, modify one or a few components, and then recompose into a matrix, or to generate a matrix from scratch from a few components.

The dictionary can contain any of the following keys: `translate`

, `rotate`

, `scale`

, `shear`

, `pivot`

, `pivot_rotate`

. The values can be hou.Vector3 objects or 3-tuples of floats.

`transform_order`

A string containing a permutation of the letters `s`

, `r`

, and `t`

.
The rotate, scale, and translate results are dependent on the order in
which you perform those operations, and this string specifies that
order.

`rotate_order`

A string containing a permutation of the letters `x`

, `y`

, and `z`

that determines the order in which rotations are performed about
the coordinate axes. This does not apply to the “pivot_rotate”

angles, which are always applied in `"xyz"`

order.

This function could be re-implemented like this:

def buildTransform(values_dict, transform_order="srt", rotate_order="xyz"): # Take the return value from explode, along with the transform and # rotate order, and rebuild the original matrix. result = hou.hmath.identityTransform() for operation_type in transform_order: if operation_type == "t": result *= hou.hmath.buildTranslate(values_dict["translate"]) elif operation_type == "s": result *= hou.hmath.buildScale(values_dict["scale"]) if "shear" in values_dict: result *= hou.hmath.buildShear(values_dict["shear"]) elif operation_type == "r": result *= hou.hmath.buildRotate(values_dict["rotate"], rotate_order) else: raise ValueError("Invalid transform order") return result

```
combineLocalTransform(local, world, parent_local=None, mode=hou.scaleInheritanceMode.Default)
```

→ hou.Matrix4

Returns a new world transform given its local and parent world transforms.

```
extractLocalTransform(world, parent_world, parent_local, mode=hou.scaleInheritanceMode.Default, effective_local=None)
```

→ hou.Matrix4

Returns a new local transform given its world and new parent transforms. If
`effective_local`

is given, then it is a hou.Matrix4 modified to be
the effective local transform taking into account `mode`

.

```
identityTransform()
```

→ hou.Matrix4

Returns the identity matrix. This is the same as `hou.Matrix4(1)`

but may make your code more understandable.

>>> hou.hmath.identityTransform() <hou.Matrix4 [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]>

See hou.Matrix4.

```
degToRad(degrees)
```

→ ```
float
```

Given a value in degrees, return the corresponding value in radians.

This function is equivalent to `degrees * math.pi / 180.0`

.

```
radToDeg(radians)
```

→ ```
double
```

Given a value in radians, return the corresponding value in degrees.

This function is equivalent to `radians * 180.0 / math.pi`

.

```
clamp(value, min, max)
```

→ ```
float
```

Returns the value clamped to the range `min`

to `max`

. See also
hou.hmath.wrap(). This function is useful in expressions to prevent
a value from going outside the specified range.

```
wrap(value, min, max)
```

Similar to the hou.hmath.clamp() function in that the resulting value will always fall between the specified minimum and maximum value. However, it will create a saw-tooth wave for continuously increasing or decreasing parameter values.

```
sign(value)
```

→ ```
int
```

Returns 1.0 if `value`

is positive, -1.0 if negative and 0.0 if `value`

is
zero.

Note that you can achieve the same effect with Python’s built-in `cmp`

function: `float(cmp(value, 0))`

.

```
smooth(value, min, max)
```

→ ```
float
```

Takes a value and range and returns a smooth interpolation between 0 and 1.

When `value`

is less than `min`

, the return value is 0.
If `value`

is greater than `max`

, the return value is 1.

>>> hou.hmath.smooth(5, 0, 20) 0.15625 >>> hou.hmath.smooth(10, 0, 20) 0.5 >>> hou.hmath.smooth(15, 0, 20) 0.84375

# Visualize the output of this function by positioning geometry objects at various locations. def createSpheres(num_spheres=40): for i in range(num_spheres): sphere = hou.node("/obj").createNode("geo").createNode("sphere") sphere.parmTuple("rad").set((0.1, 0.1, 0.1)) sphere.setDisplayFlag(True) # Given a value between 0 and 5, we'll call smooth with a range # of 0 to 3, and the resulting y value will be between 0 and 1. x = 5.0 * i / num_spheres y = hou.hmath.smooth(x, 0, 3) sphere.parent().setParmTransform(hou.hmath.buildTranslate((x, y, 0)))

```
fit(value, old_min, old_max, new_min, new_max)
```

→ ```
float
```

Returns a number between `new_min`

and `new_max`

that is relative to
the `value`

between the range `old_min`

and `old_max`

. If the value
is outside the `old_min`

to `old_max`

range, it will be clamped to the new
range.

>>> hou.hmath.fit(3, 1, 4, 5, 20) 15.0

```
fit01(value, new_min, new_max)
```

→ ```
float
```

Returns a number between `new_min`

and `new_max`

that is relative to
the `value`

between the range 0 and 1. If the value is outside the 0
to 1 range, it will be clamped to the new range.

This function is a shortcut for
`hou.hmath.fit(value, 0.0, 1.0, new_min, new_max)`

.

```
fit10(value, new_min, new_max)
```

→ ```
float
```

Returns a number between `new_min`

and `new_max`

that is relative to
the `value`

between the range 1 to 0. If the value is outside the 1 to 0
range, it will be clamped to the new range.

This function is a shortcut for
`hou.hmath.fit(value, 1.0, 0.0, new_min, new_max)`

.

```
fit11(value, new_min, new_max)
```

→ ```
float
```

Returns a number between `new_min`

and `new_max`

that is relative to
the `value`

between the range -1 to 1. If the value is outside the
-1 to 1 range, it will be clamped to the new range.

This function is a shortcut for
`hou.hmath.fit(value, -1.0, 1.0, new_min, new_max)`

.

```
rand(seed)
```

→ ```
float
```

Returns a pseudo-random number from 0 to 1. Using the same `seed`

will
always give the same result.

```
noise1d(pos)
```

→ ```
float
```

Given a sequence of 1 to 4 floats representing a position in N-dimensional space, return a single float corresponding to 1 dimensional noise.

This function matches the output of the noise function from VEX.

```
noise3d(pos)
```

→ hou.Vector3

Given a sequence of 1 to 4 floats representing a position in N-dimensional space, return a hou.Vector3 object representing the vector noise at the given position.

This function matches the output of the noise function from VEX.

```
orient2d(pa, pb, point)
```

→ ```
float
```

Performs an adaptive exact sidedness test of the 2d point against the line
defined by `pa`

and `pb`

.

See http://www.cs.cmu.edu/~quake/robust.html for details of the implementation.

```
orient3d(pa, pb, pc, point)
```

→ ```
float
```

Performs an adaptive exact sidedness test of the 3d point against the plane
defined by `pa`

, `pb`

, and `pc`

.

See http://www.cs.cmu.edu/~quake/robust.html for details of the implementation.

```
inCircle(pa, pb, pc, point)
```

→ ```
float
```

Performs an adaptive exact inside test of the 2d point against the circle
defined by `pa`

, `pb`

, and `pc`

. `pa`

, `pb`

, and `pc`

must be in counter-clockwise
order to get a positive value for interior points.

See http://www.cs.cmu.edu/~quake/robust.html for details of the implementation.

```
inSphere(pa, pb, pc, pd, point)
```

→ ```
float
```

Performs an adaptive exact inside test of the 3d point against the sphere
defined by `pa`

, `pb`

, `pc`

, and `pd`

. Note that inconsistent orientation of the
four sphere defining points will reverse the sign of the result.

See http://www.cs.cmu.edu/~quake/robust.html for details of the implementation.

```
intersectPlane(plane_point, plane_normal, line_origin, line_dir)
```

→ hou.Vector3

Takes a plane defined by an origin point and normal vector (`plane_point`

and `plane_normal`

) and a line defined by an origin and direction (`line_origin`

and `line_dir`

) and returns a hou.Vector3 value representing the XYZ coordinates of the intersection point between the line and plane. All arguments must be hou.Vector3.

hou.hmath.intersectPlane( hou.Vector3(0, 0, 0), hou.Vector3(0, 1, 0), hou.Vector3(0.212, 1.56, 0), hou.Vector3(0, 0.62, -0.34) ) # -> hou.Vector3(0.212, -1.19209e-07, 0.855484)

(Note that line runs forward and backward along the `line_dir`

from the origin. That is, even if `line_dir`

points away from the plane, you will get the intersection “behind” the origin.)

hou.hmath.intersectPlane( hou.Vector3(0, 0, 0), hou.Vector3(0, 1, 0), # Ground plane hou.Vector3(0, 1, 0), hou.Vector3(0, 1, 0) # Line up from 1u above ground ) # -> hou.Vector3(0, 0, 0)

This function raises an exception if the line is parallel to the plane, or if the `line_dir`

has no length, or even if the line is not mathematically parallel but “parallel enough” that the answer would be outside roughly a `-100000, -100000`

to `100000, 100000`

square.

```
slerpTransforms( xforms, input_weights, normalize_weights, slerp_method, slerp_flip_method)
```

→ hou.Matrix4

Spherically blend transforms by decomposing into separate quaternions. `xforms`

is the array of hou.Matrix4 transforms to blend. `input_weights`

is an array of floats with the same size as the `xforms`

. Set `normalize_weights`

to True to normalize the input weights. `slerp_method`

can be 0 to blend using normalized linear interpolation of quaternions or 1 to use an iterative method. `slerp_flip_method`

defines a flip methid for slerp to ensure consistency during blending. It can be 0 to use the hemisphere of the first quaternion, or 1 to compare each adjacent quaternions when using NLERP.