Level sets are extensively used for the visualization of scalar fields. The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. It is obtained by mapping each connected component of a level set to a point. The Reeb graph and its loop-free version called the contour tree serve as an effective user interface for selecting meaningful level sets and for designing transfer functions for volume rendering. It also finds several other applications in the field of scientific visualization. In this thesis, we focus on designing algorithms for efficiently computing the Reeb graph of scalar functions and using the Reeb graph for effective visualization of scientific data. We have developed three algorithms to compute the Reeb graph of PL functions defined over manifolds and non-manifolds in any dimension. The first algorithm efficiently tracks the connected components of the level set and has the best known theoretical bound on the running time. The second algorithm, utilizes an alternate definition of Reeb graphs using cylinder maps, is simple to implement and efficient in practice. The third algorithm aggressively employs the efficient contour tree algorithm and is efficient both theoretically, in terms of the worst case running time, and practically, in terms of performance on real-world data. This algorithm has the best performance among existing methods and computes the Reeb graph at least an order of magnitude faster than other generic algorithms. We describe a scheme for controlled simplification of the Reeb graph and two different graph layout schemes that help in the effective presentation of Reeb graphs for visual analysis of scalar fields. We also employ the Reeb graph in four different applications – surface segmentation, spatially-aware transfer function design, visualization of interval volumes, and interactive exploration of time-varying data. Finally, we introduce the notion of topological saliency that captures the relative importance of a topological feature with respect to other features in its local neighborhood. We integrate topological saliency with Reeb graph based methods and demonstrate its application to visual analysis of features.

Denna studie utforskar användningen av Re-Con Zero ballast (RCZ-ballast), ett material framställt från återvunnen betong och en tvåkomponents pulverprodukt, som ett alternativ till traditionellt jungfruligt ballastmaterial i betongproduktion. Studiens huvudsakliga syfte är att bidra till en mer hållbar och cirkulär betongindustri, där restbetong inte blir ett avfallsproblem utan en värdefull resurs. Studien vill fylla en kunskapslucka om hur RCZ-ballast påverkar betongens färska samt hårdnade egenskaper. Studien undersöker om RCZ-ballast kan matcha prestandan hos traditionellt ballastmaterial med avseende på viktiga betongegenskaper som densitet, vattenabsorption, samt mekaniska egenskaper som sättmått, lufthalt och tryckhållfasthet. Experimentella metoder inkluderade tester för att jämföra mellan betongblandningar med traditionellt ballast och den som innehåller en del RCZ-ballast. Dessa tester omfattade densitet och vattenabsorption på RCZ-ballast, dessutom mätningar av sättmått och lufthalt vid olika tider (0, 30 och 60 minuter) samt tryckhållfasthet vid olika härdningstider (1, 7 och 28 dagar) för samtliga blandningar.  Resultaten från dessa tester visade att betong framställd med RCZ-ballast generellt hade högre vattenabsorption och lägre densitet jämfört med traditionella blandningar. Trots dessa material betingade skillnader uppnådde betongen med RCZ-ballast likartade tryckhållfasthetsvärden inom ramen för ett normalfördelat material vid alla testade tidpunkter. Detta visar att RCZ-ballast anses vara lämplig med avseende på tryckhållfasthet. Slutsatserna från studien understryker att RCZ-ballast, framställt från restbetong, är ett fullt fungerande alternativ till jungfruligt bergmaterial i betong, med god tryckhållfasthet. Det finns dock tydliga skillnader i sättmått, där betongens beteende varierar beroende på om den blandas med nyproducerad eller mättad RCZ-ballast. Studien avslöjar även att både nyproducerad och mättad RCZ-ballast påverkar betongens lufthalt på olika sätt jämfört med betong som är tillverkad med jungfruligt ballastmaterial. / This study explores the use of Re-Con Zero aggregates (RCZ-aggregates), a material made from recycled concrete and a two-component powder product, as an alternative to traditional virgin aggregates material in concrete production. The primary purpose of the study is to contribute to a more sustainable and circular concrete industry, where surplus or excess  concrete does not become a waste problem but a valuable resource. The study aims to fill a knowledge gap regarding how RCZ-aggregates impacts the fresh and hardened properties of concrete. The study investigates whether RCZ-​​aggregates can match the performance of traditional aggregates materials with respect to key concrete properties such as density, water absorption, and other mechanical properties like slump, air content, and compressive strength. Experimental methods included tests to compare between concrete mixes with traditional aggregates and those containing RCZ-aggregates. These tests measured the density and water absorption of RCZ-aggregates, as well as slump and air content at different times (0, 30, and 60 minutes) and compressive strength at various curing times (1, 7, and 28 days) for all mixes. The results from these tests showed that concrete made with RCZ-aggregates generally had higher water absorption and lower density compared to traditional mixes. Despite these material-induced differences, the concrete with RCZ-aggregates achieved compressive strength values that were similarly within the range of a normally distributed material at all tested times. This demonstrates that RCZ-aggregates is considered suitable in terms of compressive strength. The conclusions from the study underscore that RCZ-aggregates , made from residual concrete, is a fully functioning alternative to virgin aggregates material in concrete, with good compressive strength. However, there are clear differences in slump, where the behavior of the concrete varies depending on whether it is mixed with newly produced or saturated RCZ-aggregates. The study also reveals that both newly produced and saturated RCZ-aggregates affect the air content of concrete differently compared to concrete made with virgin aggregates material.