python/examples/maths.py

"""
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NVIDIA CORPORATION and its licensors retain all intellectual property
and proprietary rights in and to this software, related documentation
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license agreement from NVIDIA CORPORATION is strictly prohibited.


Gym API Math
------------
Examples of math operations available in the Gym API
Demonstrates conversion to numpy data types
"""


import numpy as np
import math
from isaacgym import gymapi
a = gymapi.Vec3(2, 3, 4)
b = gymapi.Vec3(0.5, 0.25, 0.125)
print("(%f, %f, %f)" % (a.x, a.y, a.z))

c = a + b
d = a - b
e = a * 2
f = a / 2.0
print("(%f, %f, %f)" % (c.x, c.y, c.z))
print("(%f, %f, %f)" % (d.x, d.y, d.z))
print("(%f, %f, %f)" % (e.x, e.y, e.z))
print("(%f, %f, %f)" % (f.x, f.y, f.z))
print()

# Quaternions from axis-angle
qx1 = gymapi.Quat.from_axis_angle(gymapi.Vec3(1, 0, 0), 0.5 * math.pi)
qy1 = gymapi.Quat.from_axis_angle(gymapi.Vec3(0, 1, 0), 0.5 * math.pi)
qz1 = gymapi.Quat.from_axis_angle(gymapi.Vec3(0, 0, 1), 0.5 * math.pi)
print("(%f, %f, %f, %f)" % (qx1.x, qx1.y, qx1.z, qx1.w))
print("(%f, %f, %f, %f)" % (qy1.x, qy1.y, qy1.z, qy1.w))
print("(%f, %f, %f, %f)" % (qz1.x, qz1.y, qz1.z, qz1.w))
print()

# Quaternions from roll, pitch, yaw
qx2 = gymapi.Quat.from_euler_zyx(0.5 * math.pi, 0, 0)
qy2 = gymapi.Quat.from_euler_zyx(0, 0.5 * math.pi, 0)
qz2 = gymapi.Quat.from_euler_zyx(0, 0, 0.5 * math.pi)
print("(%f, %f, %f, %f)" % (qx2.x, qx2.y, qx2.z, qx2.w))
print("(%f, %f, %f, %f)" % (qy2.x, qy2.y, qy2.z, qy2.w))
print("(%f, %f, %f, %f)" % (qz2.x, qz2.y, qz2.z, qz2.w))
print()

# Roll, pitch, yaw from quaternions
r1, p1, y1 = qx2.to_euler_zyx()
r2, p2, y2 = qy2.to_euler_zyx()
r3, p3, y3 = qz2.to_euler_zyx()
print("%f, %f, %f" % (r1, p1, y1))
print("%f, %f, %f" % (r2, p2, y2))
print("%f, %f, %f" % (r3, p3, y3))
print()

# Quaternion multiplication and normalization
qxy = (qx1 * qy2).normalize()

c = qx1.rotate(a)
d = qy1.rotate(a)
e = qxy.rotate(a)
print("(%f, %f, %f)" % (a.x, a.y, a.z))
print("(%f, %f, %f)" % (c.x, c.y, c.z))
print("(%f, %f, %f)" % (d.x, d.y, d.z))
print("(%f, %f, %f)" % (e.x, e.y, e.z))
print()

# Quaternion inverse
qx1_inv = qx1.inverse()
qx1_inv_inv = qx1_inv.inverse()
print(qx1)
print(qx1_inv)
print(qx1_inv_inv)
print()

# Vector magnitude and direction
length = a.length()
d = a.normalize()
print("%f" % length)
print("(%f, %f, %f)" % (d.x, d.y, d.z))
print()

# Dot and cross products
dp = a.dot(b)
cp = a.cross(b)
print("%f" % dp)
print("(%f, %f, %f)" % (cp.x, cp.y, cp.z))
print()

# Transforms
tx = gymapi.Transform(b, qx1)
c = tx.transform_point(a)
e = tx.transform_vector(d)
print("(%f, %f, %f)" % (c.x, c.y, c.z))
print("(%f, %f, %f)" % (e.x, e.y, e.z))
print()

# Inverse transforms
tx_inv = tx.inverse()
tx_inv_inv = tx_inv.inverse()
print(tx.p, tx.r)
print(tx_inv.p, tx_inv.r)
print(tx_inv_inv.p, tx_inv_inv.r)
print()

# Access gym data types as structured arrays
print(gymapi.Vec3.dtype)
print(gymapi.Quat.dtype)
print(gymapi.Transform.dtype)
print()

# Convert a gym data type to a numpy array
arr = np.zeros(2, dtype=gymapi.Transform.dtype)
print(arr)
print(arr['p'])
print(arr['r'])
print()

# Accesing components of translation and rotation from transform and writing to structured arrays
arr[0] = ((tx.p.x, tx.p.y, tx.p.z), (tx.r.x, tx.r.y, tx.r.z, tx.r.w))
arr['p'][1] = (1, 2, 3)
arr['r'][1] = (0, 0, 0, 1)
print(arr)
print(arr[0])
print(arr[1])
print()

# Reading from structured arrays
pose1 = gymapi.Transform.from_buffer(arr[0])
pose2 = gymapi.Transform.from_buffer(arr[1])
print("(%f, %f, %f) (%f, %f, %f, %f)" % (pose1.p.x, pose1.p.y, pose1.p.z,
                                         pose1.r.x, pose1.r.y, pose1.r.z, pose1.r.w))
print("(%f, %f, %f) (%f, %f, %f, %f)" % (pose2.p.x, pose2.p.y, pose2.p.z,
                                         pose2.r.x, pose2.r.y, pose2.r.z, pose2.r.w))
print()