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An orthographic drawing is also called a multiview drawing. It is typically measured with cognitive tests and is a predictor of success in STEM fields. Also referred to as visual-spatial ability. Used in making isometric sketches. Also called isometric paper. Worksheet: After completing the classroom instructions and group exercises, have students complete the Orthographic Drawings Worksheet. Observe whether students are able to draw the objects or if they are struggling. Assist them as necessary. Review their answers to gauge their depth of understanding. Discussion: Ask students to explain and describe their drawings with specific focus on orthographic views. What strategies did they use to draw their cube shapes? What were the limitations they experienced, if any? How did students solve any drawing challenges? Students learn about isometric drawings and practice sketching on triangle-dot paper the shapes they make using multiple simple cubes.

They also learn how to use coded plans to envision objects and draw them on triangle-dot paper. In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided question quiz. Following the lesson, students complete the four associated spatial visualization activities and then re-take the quiz to see how mu Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis ro This lesson plan and its associated activities were derived from a summer workshop taught by Jacob Segil for undergraduate engineers at the University of Colorado Boulder.

The activities have been adapted to suit the skill level of middle school students, with suggestions on how to adapt activities to elementary or, in some instances, high school level. Toggle navigation. Why Teach Engineering in K? Find more at TeachEngineering. Quick Look. Print this activity. Suggest an edit. Discuss this activity. Activities Associated with this Lesson Units serve as guides to a particular content or subject area. TE Newsletter. Subscribe to TE Newsletter. Summary Students learn how to create two-dimensional representations of three-dimensional objects by utilizing orthographic projection techniques. They build shapes using cube blocks and then draw orthographic and isometric views of those shapes—which are the side views, such as top, front, right—with no depth indicated. Then working in pairs, one blindfolded partner describes a shape by feel alone as the other partner draws what is described. A worksheet is provided.

This activity is part of a multi-activity series towards improving spatial visualization skills. Draw, construct, and describe geometrical figures and describe the relationships between them. Grade 7 More Details View aligned curriculum Do you agree with this alignment? Verify experimentally the properties of rotations, reflections, and translations: Grade 8 More Details View aligned curriculum Do you agree with this alignment? Apply geometric concepts in modeling situations Grades 9 - 12 More Details View aligned curriculum Do you agree with this alignment? Visualize relationships between two-dimensional and three-dimensional objects Grades 9 - 12 More Details View aligned curriculum Do you agree with this alignment? Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Grades 9 - 12 More Details View aligned curriculum Do you agree with this alignment?

Colorado - Math Modeling geometric figures and relationships leads to informal spatial reasoning and proof. Verify experimentally the properties of rotations, reflections, and translations. Grade 8 More Details View aligned curriculum Do you agree with this alignment? Objects in the real world can be modeled using geometric concepts. Visualize relationships between two-dimensional and three-dimensional objects. Spatial Visualization Practice Quiz pdf. Spatial Visualization Presentation pptx. Spatial Visualization Presentation pdf. Image tie points are generated in the overlap areas between adjacent images composing the mosaic. These points serve to tie together all the imagery comprising the orthoimage mosaic. These are usually computed automatically using image matching techniques in the overlap area. Check points are used for assessing the accuracy of the orthorectification process. These are ground control survey points not used in computing the photogrammetric adjustment.

The information above is used to compute an image orientation needed to produce a DEM and an orthorectified image mosaic from imagery. The derived image orientation parameters include the position of the sensor at the instant of image capture in coordinates such as latitude, longitude, and height x, y, z. The attitude of the sensor is expressed as omega, phi, and kappa pitch, roll, heading. The general workflow to generate an orthomosaic is outlined in this section. Image orientation is a prerequisite for generating DEMs and orthoimagery. It is a process of determining the spatial position and orientation of the sensor at the time each image was captured. Knowing the height of the sensor above the ground allows calculation of the overlap regions of adjacent images, which is then used to enable tie point generation. The tie point generation process will place all the images correctly into a contiguous block. It uses the interior orientation based on physical sensor characteristics and exterior orientation based on ground control and tie points between images.

Collecting tie points between multiple overlapping images can be tedious and time consuming. The Compute Tie Points tool automatically identifies coincident points in the overlap areas between images using cross-correlation techniques.

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These tie points are used together with ground control points, which are also visible in multiple images, to compute the exterior orientation of each image comprising the mosaic. This means that the ground control must be photo-identifiable or visible in the imagery. Typical photo-identifiable ground control points are persistent and readily identifiable features. They may be painted targets on a highway or the center of two intersecting streets. Using the ground control and tie point information, a bundle adjustment computation calculates the exterior orientation for each image, such that they are consistent with neighboring images. The orientation for the whole block of images is then adjusted to fit the ground. This block adjustment process produces the best statistical fit between images, for the whole contiguous block, minimizing errors with the tie points and ground control. The adjusted transformation for each image item comprising the block is recorded in the solutions table and stored in the workspace for the orthomosaic.

When the block of images is adjusted to fit the ground, the apparent error of the adjusted points is presented in a table of residual errors. Blunders are readily identified, and the points with high-residual error are either deleted or more often manually repositioned. The adjustment is recomputed until both the overall error and residual error of each point is acceptable. Once the block adjustment orientation is completed, an elevation dataset can be produced using the DEMs wizard. A photogrammetric point cloud is created to produce the DEM using image cross-correlation techniques. The DEM is then used in the image orthorectification process to remove terrain distortions and produce an orthomosaic. This is also referred to as bare-earth elevation. The bare earth DTM dataset is used to produce the orthoimage and orthomosaics. DSM—Digital elevation of the earth, including the elevation of objects on it such as trees and buildings. The DSM is a valuable analytical dataset used for classifying features in orthoimages, such as discriminating asphalt pavement and asphalt roofs.

It should not be used for image orthorectification unless the source imagery is nadir looking, with no building or feature lean, to produce true orthoimages. Note: If a forest area is heavily wooded, or has other dense vegetation cover, it will not be possible to derive a DTM ground surface because the ground is not visible. The most appropriate elevation surface product for densely forested land cover is a DSM, which specifically creates a surface depicting the top of the tree canopy. The DTM is then used in the image orthorectification process to remove terrain distortions and produce an orthomosaic. An orthorectified image has a constant scale such that features are represented in their true positions in relation to their ground position. This enables accurate measurement of distances, angles, and areas in the orthoimage. Orthorectification is accomplished by establishing the relationship of the x,y image coordinates to the real-world GCP to determine the algorithm for resampling the image.

Similarly, the mathematical relationship between the ground coordinates, represented by the DTM, and the image is computed and used to determine the proper position of each pixel in the source image. The orthomosaic is produced using the Orthomosaic wizard. The inputs include the block-adjusted items comprising the image collection and the DTM. An existing bare earth DEM can also be used. The Orthomosaic wizard allows you to define the settings for mosaicking your orthoimages such as scale and data format, seamline generation, and color balancing between orthorectified images to create a seamless orthomosaic. Note: Nadir high-resolution satellite imagery is not affected much by distortion that is inherent in aerial imagery due to the large distance between sensor and ground, long sensor focal length on the order of 10 meters , and small field of view.

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These factors, together with accurate orientation information in the form of RPCs, result in the condition that DEM accuracy and dense postings are less important in producing accurate orthoimages, as long as the adjusted exterior orientation and control points are adequate. If the off-nadir collection is large, or the focal length is small, a more accurate, higher resolution DEM is needed for accurate orthorectification. The types of artifacts that affect remotely sensed imagery, and addressed in the orthorectification process, are briefly described in the table below. Perspective distortion is affected by the look angle of obliquity and distance between the sensor and the ground target, as well as sensor characteristics. The short focal lengths of airborne sensors exhibit more perspective distortion than the long focal lengths of the satellite-based senors. The viewing perspective will show the sides of buildings facing the sensor and mask the back sides of buildings.

Additionally, in perspective images, the scale of the image gets smaller as you move away from the nadir. In other words, the ground sample distance GSD is smaller toward the image nadir and larger toward the far edge of the image, and the pixels are trapezoidal in shape.

Multiview projection

FoV is the angular extent that is visible to the sensor during exposure. It is determined by the sensor size, focal length, and altitude. Focal length is the effective distance from the lens rear nodal point to the focal plane. This determines the perspective geometry of the image. The shorter the focal length, the more perspective distortion is introduced and the wider the FoV. Lenses only approximate perspective geometry. As a result, they distort the placement and shape of objects imaged on the focal plane. Radiometrically, they also vary the amount of light reaching the focal plane. Both types of distortion increase as a function of the distance from the center of the image. These effects are minimized at the center and increase toward the edge of the image. Distortion induced by earth curvature is most prevalent in images that cover wide extents of the earth, or look out at high oblique angles from high altitude. It usually affects aerial imagery collected with a short focal length, at high altitude, with a wide FoV, or satellite imagery in strips or blocks.

Relief displacement is caused by variable elevation above or below a particular datum, which results in a shift in the object's apparent position in the image. This topographic variation, coupled with view orientation and FoV of the sensor, affects the distance and scale with which features are displayed on the imagery. For example, in vertical imagery, tall objects like radio towers will appear lean out from the center nadir point of the imagery. Since the top of the tower does not lie under the bottom of the tower in the imagery, the effect is referred to as relief displacement. When scanning aerial photography, distortions are first introduced in film processing and storage. Then additional distortions may be introduced in the scanning process due to lens or other scanning instrumentation. These errors must be largely compensated for in the orthorectification process. Feedback on this topic? Back to Top. Available with Advanced license. Overview Photogrammetry is the science of obtaining reliable measurements from photographs and digital imagery.

Orthoimagery Orthorectification is a process that corrects for many artifacts related to remotely sensed imagery to produce a map-accurate orthoimage. Elevation data If a suitable digital elevation model DEM exists, it will be used in the orthorectification process. The need for ortho mapping Orthorectification refers to the removal of geometric inaccuracies induced by the platform, sensor, and especially terrain displacement. The orthorectification process One of the most important products generated by the photogrammetric process is an orthorectified collection of images, called an orthoimage mosaic, or simply orthomosaic.