lib/renderer/camera.py

# -*- coding: utf-8 -*-

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#
# Copyright©2019 Max-Planck-Gesellschaft zur Förderung
# der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute
# for Intelligent Systems. All rights reserved.
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# Contact: ps-license@tuebingen.mpg.de

import cv2
import numpy as np

from .glm import ortho


class Camera:

    def __init__(self, width=1600, height=1200):
        # Focal Length
        # equivalent 50mm
        focal = np.sqrt(width * width + height * height)
        self.focal_x = focal
        self.focal_y = focal
        # Principal Point Offset
        self.principal_x = width / 2
        self.principal_y = height / 2
        # Axis Skew
        self.skew = 0
        # Image Size
        self.width = width
        self.height = height

        self.near = 1
        self.far = 10

        # Camera Center
        self.center = np.array([0, 0, 1.6])
        self.direction = np.array([0, 0, -1])
        self.right = np.array([1, 0, 0])
        self.up = np.array([0, 1, 0])

        self.ortho_ratio = None

    def sanity_check(self):
        self.center = self.center.reshape([-1])
        self.direction = self.direction.reshape([-1])
        self.right = self.right.reshape([-1])
        self.up = self.up.reshape([-1])

        assert len(self.center) == 3
        assert len(self.direction) == 3
        assert len(self.right) == 3
        assert len(self.up) == 3

    @staticmethod
    def normalize_vector(v):
        v_norm = np.linalg.norm(v)
        return v if v_norm == 0 else v / v_norm

    def get_real_z_value(self, z):
        z_near = self.near
        z_far = self.far
        z_n = 2.0 * z - 1.0
        z_e = 2.0 * z_near * z_far / (z_far + z_near - z_n * (z_far - z_near))
        return z_e

    def get_rotation_matrix(self):
        rot_mat = np.eye(3)
        s = self.right
        s = self.normalize_vector(s)
        rot_mat[0, :] = s
        u = self.up
        u = self.normalize_vector(u)
        rot_mat[1, :] = -u
        rot_mat[2, :] = self.normalize_vector(self.direction)

        return rot_mat

    def get_translation_vector(self):
        rot_mat = self.get_rotation_matrix()
        trans = -np.dot(rot_mat, self.center)
        return trans

    def get_intrinsic_matrix(self):
        int_mat = np.eye(3)

        int_mat[0, 0] = self.focal_x
        int_mat[1, 1] = self.focal_y
        int_mat[0, 1] = self.skew
        int_mat[0, 2] = self.principal_x
        int_mat[1, 2] = self.principal_y

        return int_mat

    def get_projection_matrix(self):
        ext_mat = self.get_extrinsic_matrix()
        int_mat = self.get_intrinsic_matrix()

        return np.matmul(int_mat, ext_mat)

    def get_extrinsic_matrix(self):
        rot_mat = self.get_rotation_matrix()
        int_mat = self.get_intrinsic_matrix()
        trans = self.get_translation_vector()

        extrinsic = np.eye(4)
        extrinsic[:3, :3] = rot_mat
        extrinsic[:3, 3] = trans

        return extrinsic[:3, :]

    def set_rotation_matrix(self, rot_mat):
        self.direction = rot_mat[2, :]
        self.up = -rot_mat[1, :]
        self.right = rot_mat[0, :]

    def set_intrinsic_matrix(self, int_mat):
        self.focal_x = int_mat[0, 0]
        self.focal_y = int_mat[1, 1]
        self.skew = int_mat[0, 1]
        self.principal_x = int_mat[0, 2]
        self.principal_y = int_mat[1, 2]

    def set_projection_matrix(self, proj_mat):
        res = cv2.decomposeProjectionMatrix(proj_mat)
        int_mat, rot_mat, camera_center_homo = res[0], res[1], res[2]
        camera_center = camera_center_homo[0:3] / camera_center_homo[3]
        camera_center = camera_center.reshape(-1)
        int_mat = int_mat / int_mat[2][2]

        self.set_intrinsic_matrix(int_mat)
        self.set_rotation_matrix(rot_mat)
        self.center = camera_center

        self.sanity_check()

    def get_gl_matrix(self):
        z_near = self.near
        z_far = self.far
        rot_mat = self.get_rotation_matrix()
        int_mat = self.get_intrinsic_matrix()
        trans = self.get_translation_vector()

        extrinsic = np.eye(4)
        extrinsic[:3, :3] = rot_mat
        extrinsic[:3, 3] = trans
        axis_adj = np.eye(4)
        axis_adj[2, 2] = -1
        axis_adj[1, 1] = -1
        model_view = np.matmul(axis_adj, extrinsic)

        projective = np.zeros([4, 4])
        projective[:2, :2] = int_mat[:2, :2]
        projective[:2, 2:3] = -int_mat[:2, 2:3]
        projective[3, 2] = -1
        projective[2, 2] = (z_near + z_far)
        projective[2, 3] = (z_near * z_far)

        if self.ortho_ratio is None:
            ndc = ortho(0, self.width, 0, self.height, z_near, z_far)
            perspective = np.matmul(ndc, projective)
        else:
            perspective = ortho(-self.width * self.ortho_ratio / 2,
                                self.width * self.ortho_ratio / 2,
                                -self.height * self.ortho_ratio / 2,
                                self.height * self.ortho_ratio / 2, z_near,
                                z_far)

        return perspective, model_view


def KRT_from_P(proj_mat, normalize_K=True):
    res = cv2.decomposeProjectionMatrix(proj_mat)
    K, Rot, camera_center_homog = res[0], res[1], res[2]
    camera_center = camera_center_homog[0:3] / camera_center_homog[3]
    trans = -Rot.dot(camera_center)
    if normalize_K:
        K = K / K[2][2]
    return K, Rot, trans


def MVP_from_P(proj_mat, width, height, near=0.1, far=10000):
    '''
    Convert OpenCV camera calibration matrix to OpenGL projection and model view matrix
    :param proj_mat: OpenCV camera projeciton matrix
    :param width: Image width
    :param height: Image height
    :param near: Z near value
    :param far: Z far value
    :return: OpenGL projection matrix and model view matrix
    '''
    res = cv2.decomposeProjectionMatrix(proj_mat)
    K, Rot, camera_center_homog = res[0], res[1], res[2]
    camera_center = camera_center_homog[0:3] / camera_center_homog[3]
    trans = -Rot.dot(camera_center)
    K = K / K[2][2]

    extrinsic = np.eye(4)
    extrinsic[:3, :3] = Rot
    extrinsic[:3, 3:4] = trans
    axis_adj = np.eye(4)
    axis_adj[2, 2] = -1
    axis_adj[1, 1] = -1
    model_view = np.matmul(axis_adj, extrinsic)

    zFar = far
    zNear = near
    projective = np.zeros([4, 4])
    projective[:2, :2] = K[:2, :2]
    projective[:2, 2:3] = -K[:2, 2:3]
    projective[3, 2] = -1
    projective[2, 2] = (zNear + zFar)
    projective[2, 3] = (zNear * zFar)

    ndc = ortho(0, width, 0, height, zNear, zFar)

    perspective = np.matmul(ndc, projective)

    return perspective, model_view