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TABLE 410 Quality Assurance Requirements: Minimum Inspection Per IBC for Level 2 Inspection Task From the beginning of masonry construction, the following shall be verified to ensure compliance: Proportions of site prepared mortar and grout Placement of masonry units and construction of mortar joints Placement of reinforcement and connectors Grout space prior to grouting Placement of grout The inspection program shall verify: Size and location of structural elements Type, size and location of anchors, including details of anchorage of masonry to structural members, frames or other construction Specified size, grade and type of reinforcement Welding of reinforcing bars Protection of masonry during cold weather (below 40 F) or hot weather (above 90 F) Preparation of any required grout specimens, mortar specimens and/or prisms shall be observed Compliance with required inspection provisions of construction documents and approved submittals shall be verified * Frequency of inspection: P = periodically during task listed C = continuous during task listed

(1289)

and transform each cloud of points to a bundle of vectors about the centroid: (1290) The scale parameter can be determined by computing the mean length of the vectors in each bundle: (1291) The scale factor can be computed without knowing either the rotation or the translation This is a very useful formula for calibrating the baseline distance in binocular stereo and is more accurate than using only a few points After the rotation and scale factor are determined, the translation can be easily computed from the centroids: (1292) Computing the rotation is essentially the problem of determining how to align the bundles of rays about the centroids Form the matrix M from the sum of scalar products of the coodinates of the rays in the first and second views: n

(1293)

(International Building Code 2000)

MS-l,

(1294) (1295)

S = Q1/2

Freq*

(1296)

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The eigenvalues of MT M are obtained by solving a cubic equation The roots of the cubic equation can be computed from direct formulas [197J Use the eigenvalues to solve the linear equations (1297)

and testing that are required by both MSJC and IBC for each level of quality assurance are shown in Table 47 Quality assurance Level 1 is the lowest level, and quality assurance Level 3 is the highest Although IBC and MSJC agree in spirit about the extent of inspection required in each level of Quality Assurance, details of the inspection requirements differ slightly in those two documents Table 48 lists the inspection requirements as shown in MSJC Level 2 can be characterized as periodic inspection, while Level 3 is characterized as continuous inspection In this context, continuous is defined to mean that whenever a mason contractor is working on site, an inspector is also required to be on site It does not mean that every individual masonry unit and every accessory item must be observed as it is placed In IBC, no special inspection is required

for the orthogonal eigenvectors VI, V2, and V3 Matrix S is the square root of matrix Q Fortunately, matrix square roots and their inverses are easy to compute in the eigensystem representation (Equation 1296) The inverse of matrix S is (1298) Compute the outer products of the eigenvectors, divided by the square root of the eigenvectors, and multiply this matrix by M to get the rotation matrix R This method of construction guarantees that matrix R will be an orthonormal matrix This algorithm provides a closed form (noniterative) solution for the rotation matrix The scale can be determined without determining either the translation or rotation using the formula in Equation 1291 and, finally, the translation can be determined using the formula in Equation 1292 The transformation in Equation 1286 can be applied to the point measurements from any depth measurement system, including binocular stereo or a range camera, to align the point measurements to an absolute coordinate system and convert the measurements into the units of the absolute coordinate system The measurement units will be whatever system of units was used for the coordinates of the calibration points used for the absolute orientation problem For example, if the calibration points in the absolute coordinate system are in millimeters and the depth measurements are from binocular stereo with a unit baseline, then the rigid body transformation obtained by solving the absolute orientation problem with these calibration points will transform stereo measurements to millimeters The system of measurement must be the same along each coordinate axis since the same scale factor s is applied to each coordinate

The problem of exterior orientation is to determine the relationship between image plane coordinates (x', y') and the coordinates (x, y, z) of scene points in an absolute coordinate system The exterior orientation problem is called

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